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23.2: Electromagnetic Waves and their Properties

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• Explain the meaning and importance of Maxwell’s equations

Maxwell’s Equations

Maxwell’s equations are a set of four partial differential equations that, along with the Lorentz force law, form the foundation of classical electrodynamics, classical optics, and electric circuits.

Named after esteemed physicist James Clerk Maxwell, the equations describe the creation and propagation of electric and magnetic fields. Fundamentally, they describe how electric charges and currents create electric and magnetic fields, and how they affect each other.

Maxwell’s equations can be divided into two major subsets. The first two, Gauss’s law and Gauss’s law for magnetism, describe how fields emanate from charges and magnets respectively. The other two, Faraday’s law and Ampere’s law with Maxwell’s correction, describe how induced electric and magnetic fields circulate around their respective sources.

Each of Maxwell’s equations can be looked at from the “microscopic” perspective, which deals with total charge and total current, and the “macroscopic” set, which defines two new auxiliary fields that allow one to perform calculations without knowing microscopic data like atomic-level charges.

Gauss’s Law

Gauss’s law relates an electric field to the charge(s) that create(s) it. The field (E) points towards negative charges and away from positive charges, and from the microscopic perspective, is related to charge density (ρ) and vaccuum permittivity (ε 0 , or permittivity of free space) as:

\[\nabla \cdot \mathbf { E } = \dfrac { \rho } { \epsilon _ { 0 } }\]

Gauss’s Law basically says that a net amount of charge contained within a region of space will generate an electric field that emanates through the surface that surrounds that region.

Example of Gauss’s Law : A positive charge contained within a region of space creates an electric field that emanates from the surface of that region.

Gauss’s Law for Magnetism

Gauss’s law for magnetism states that there are no “magnetic charges (or monopoles)” analogous to electric charges, and that magnetic fields are instead generated by magnetic dipoles . Such dipoles can be represented as loops of current, but in many ways are similar in appearance to positive and negative “magnetic charges” that are inseparable and thus have no formal net “magnetic charge.”

Magnetic field lines form loops such that all field lines that go into an object leave it at some point. Thus, the total magnetic flux through a surface surrounding a magnetic dipole is always zero.

Field lines caused by a magnetic dipole : The field lines created by this magnetic dipole either form loops or extend infinitely.

The differential form of Gauss’s law for magnetic for magnetism is

\[\nabla \cdot \mathbf { B } = \mathbf { 0 }\]

Faraday’s Law

Faraday’s law describes how a time-varying magnetic field (or flux) induces an electric field. The principle behind this phenomenon is used in many electric generators. Both macroscopic and microscopic differential equations are the same, relating electric field (E) to the time-partial derivative of magnetic field (B):

\[\nabla \times \mathbf { E } = - \frac { \partial \mathbf { B } } { \partial \mathbf { t } }\]

Ampere’s Circuital Law (with Maxwell’s correction)

Ampere’s law originally stated that magnetic field could be created by electrical current. Maxwell added a second source of magnetic fields in his correction: a changing electric field (or flux), which would induce a magnetic field even in the absence of an electrical current. He named the changing electric field “displacement current.”

Maxwell’s correction shows that self-sustaining electromagnetic waves (light) can travel through empty space even in the absence of moving charges or currents, with the electric field component and magnetic field component each continually changing and each perpetuating the other.

Electromagnetic Waves : Electric (red) and magnetic (blue) waves propagate in phase sinusoidally, and perpendicularly to one another.

The microscopic approach to the Maxwell-corrected Ampere’s law relates magnetic field (B) to current density (J, or current per unit cross sectional area) and the time-partial derivative of electric field (E):

\[\nabla \times \mathbf { B } = \mu _ { 0 } \mathbf { J } + \mu _ { 0 } \epsilon _ { 0 } \frac { \partial \mathbf { E } } { \partial t }\]

The Production of Electromagnetic Waves

Electromagnetic waves are the combination of electric and magnetic field waves produced by moving charges.

• Explain the self-perpetuating behavior of an electromagnetic wave

Electromagnetic waves

Electromagnetic radiation, is a form of energy emitted by moving charged particles. As it travels through space it behaves like a wave, and has an oscillating electric field component and an oscillating magnetic field. These waves oscillate perpendicularly to and in phase with one another.

Electromagnetic Wave : Electromagnetic waves are a self-propagating transverse wave of oscillating electric and magnetic fields. The direction of the electric field is indicated in blue, the magnetic field in red, and the wave propagates in the positive x-direction. Notice that the electric and magnetic field waves are in phase.

The creation of all electromagnetic waves begins with a charged particle. This charged particle creates an electric field (which can exert a force on other nearby charged particles). When it accelerates as part of an oscillatory motion, the charged particle creates ripples, or oscillations, in its electric field, and also produces a magnetic field (as predicted by Maxwell’s equations).

Once in motion, the electric and magnetic fields created by a charged particle are self-perpetuating—time-dependent changes in one field (electric or magnetic) produce the other. This means that an electric field that oscillates as a function of time will produce a magnetic field, and a magnetic field that changes as a function of time will produce an electric field. Both electric and magnetic fields in an electromagnetic wave will fluctuate in time, one causing the other to change.

Electromagnetic waves are ubiquitous in nature (i.e., light) and used in modern technology—AM and FM radio, cordless and cellular phones, garage door openers, wireless networks, radar, microwave ovens, etc. These and many more such devices use electromagnetic waves to transmit data and signals.

All the above sources of electromagnetic waves use the simple principle of moving charge, which can be easily modeled. Placing a coin in contact with both terminals of a 9-volt battery produces electromagnetic waves that can be detected by bringing the antenna of a radio (tuned to a static-producing station) within a few inches of the point of contact.

Energy and Momentum

Electromagnetic waves have energy and momentum that are both associated with their wavelength and frequency.

• Relate energy of an electromagnetic wave with the frequency and wavelength

Electromagnetic radiation can essentially be described as photon streams. These photons are strictly defined as massless, but have both energy and surprisingly, given their lack of mass, momentum, which can be calculated from their wave properties.

Waves were poorly understood until the 1900s, when Max Planck and Albert Einstein developed modern corrections to classical theory.

Planck theorized that “black bodies” (thermal radiators) and other forms of electromagnetic radiation existed not as spectra, but in discrete, “quantized” form. In other words, there were only certain energies an electromagnetic wave could have. In his work he developed what is now known as “Planck’s constant,” which is approximately equal to 6.626×10 -34 J·s.

The energy (E) of a photon can be related to its frequency (f) by Planck’s constant (h):

\[\mathrm { E } = \mathrm { hf } = \frac { \mathrm { hc } } { \lambda }\]

The ratio of speed of light (c) to wavelength (λ) can be substituted in place of f to give the same equation to energy in different terms. Note that energy cannot take any value: it can only exist in increments of frequency times Planck’s constant (or Planck’s constant times c divided by wavelength). Energy of a wave is therefore “quantized. ”

Wavelength : Wavelength of the sinusoidal function is represented by λ.

Momentum is classically defined as the product of mass and velocity and thus would intuitively seem irrelevant to a discussion of electromagnetic radiation, which is both massless and composed of waves.

However, Einstein proved that light can act as particles in some circumstances, and that a wave-particle duality exists. And, given that he related energy and mass (E=mc 2 ), it becomes more conceivable that a wave (which has an energy value) not only has an equation to mass but a momentum as well.

And indeed, Einstein proved that the momentum (p) of a photon is the ratio of its energy to the speed of light.

\[\mathrm { p } = \dfrac { \mathrm { E } } { \mathrm { c } } = \dfrac { \mathrm { hf } } { \mathrm { c } } = \dfrac { \mathrm { h } } { \lambda }\]

Substituting E with hc/λ cancels the c terms, making momentum also equal to the simple ratio of Planck’s constant to wavelength.

The Speed of Light

The speed of light in a vacuum is one of the most fundamental constant in physics, playing a pivotal role in modern physics.

• Relate speed of light with the index of refraction of the medium

The speed of light is generally a point of comparison to express that something is fast. shows a scale representation of the time it takes a beam of light to reach the moon from Earth. But what exactly is the speed of light?

Light Going from Earth to the Moon : A beam of light is depicted travelling between the Earth and the Moon in the time it takes a light pulse to move between them: 1.255 seconds at their mean orbital (surface-to-surface) distance. The relative sizes and separation of the Earth–Moon system are shown to scale.

It is just that: the speed of a photon or light particle. The speed of light in a vacuum (commonly written as c) is 299,792,458 meters per second. This is a universal physical constant used in many areas of physics. For example, you might be familiar with the equation:

\[\mathrm { E } = \mathrm { mc } ^ { 2 }\]

where E = Energy and m = mass. This is known as the mass-energy equivalence, and it uses the speed of light to interrelate space and time. This not only explains the energy a body of mass contains, but also explains the hindrance mass has on speed.

There are many uses for the speed of light in a vacuum, such as in special relativity, which says that c is the natural speed limit and nothing can move faster than it. However, we know from our understanding of physics (and previous atoms) that the speed at which something travels also depends on the medium through which it is traveling. The speed at which light propagates through transparent materials (air, glass, etc.,) is dependent on the refractive index of that material, n:

\[\mathrm { v } = \dfrac { \mathrm { c } } { \mathrm { n } }\]

where v = actual velocity of light moving through the medium, c = speed of light in a vacuum, and n = refractive index of medium. The refractive index of air is about 1.0003, and from this equation we can find that the speed of visible light in air is about 90 km/s slower than c.

As mentioned earlier, the speed of light (usually of light in a vacuum) is used in many areas of physics. Below is an example of an application of the constant c.

The Lorentz Factor

Fast-moving objects exhibit some properties that are counterintuitive from the perspective of classical mechanics. For example, length contracts and time dilates (runs slower) for objects in motion. The effects are typically minute, but are noticeable at sufficiently high speeds. The Lorentz factor (γ) is the factor by which length shortens and time dilates as a function of velocity (v):

\[\gamma = \left( 1 - \mathrm{ v } ^ { 2 } / \mathrm { c } ^ { 2 } \right) ^ { - 1 / 2 } \gamma = \left( 1 - \mathrm { v } ^ { 2 } / \mathrm { c } ^ { 2 } \right) ^ { - 1 / 2 } \gamma = \left( 1 - \mathrm { v } ^ { 2 } / \mathrm { c } ^ { 2 } \right) ^ { - 1 / 2 }\]

At low velocities, the quotient of v 2 /c 2 is sufficiently close to 0 such that γ is approximately 1. However, as velocity approaches c, γ increases rapidly towards infinity.

The Doppler Effect

The Doppler Effect is the change in a wave’s perceived frequency that results from the source’s motion, the observer, and the medium.

• Give examples of daily observations of the Doppler effect

The Doppler effect is a periodic event’s change in frequency for an observer in motion relative to the event’s source. Typically, this periodic event is a wave.

Most people have experienced the Doppler effect in action. Consider an emergency vehicle in motion, sounding its siren. As it approaches an observer, the pitch of the sound (its frequency) sounds higher than it actually is. When the vehicle reaches the observer, the pitch is perceived as it actually is. When the vehicle continues away from the observer, the pitch is perceived as lower than it actually is. From the perspective of an observer inside the vehicle, the pitch of the siren is constant.

The Doppler Effect and Sirens : Waves emitted by a siren in a moving vehicle

The difference in the perceived pitch depending on observer location can be explained by the fact that the siren’s position changes as it emits waves. A wave of sound is emitted by a moving vehicle every millisecond. The vehicle ‘chases’ each wave in one direction. By the time the next wave is emitted, it is closer (relative to an onlooker ahead of the vehicle) to the previous wave than the wave’s frequency would suggest. Relative to an onlooker behind the vehicle, the second wave is further from the first wave than one would expect, which suggests a lower frequency.

The Doppler effect can be caused by any kind of motion. In the example above, the siren moved relative to a stationary observer. If the observer moves relative to the stationary siren, the observer will notice the Doppler effect on the pitch of the siren. Finally, if the medium through which the waves propagate moves, the Doppler effect will be noticed even for a stationary observer. An example of this phenomenon is wind.

Quantitatively, the Doppler effect can be characterized by relating the frequency perceived (f) to the velocity of waves in the medium (c), the velocity of the receiver relative to the medium (v r ), the velocity of the source relative to the medium (v s ), and the actual emitted frequency (f 0 ):

\[\mathrm { f } = \left( \dfrac { \mathrm { c } + \mathrm { v } _ { \mathrm { r } } } { \mathrm { c } + \mathrm { v } _ { \mathrm { s } } } \right) \mathrm { f } _ { 0 }\]

The Doppler Effect : Wavelength change due to the motion of source

Momentum Transfer and Radiation Pressure Atom

Radiation pressure is the pressure exerted upon any surface exposed to electromagnetic (EM) radiation.

• Explain formation of radiation pressure

Radiation pressure is the pressure exerted upon any surface exposed to electromagnetic (EM) radiation. EM radiation (or photon, which is a quantum of light) carries momentum; this momentum is transferred to an object when the radiation is absorbed or reflected. Perhaps one of the most well know examples of the radiation pressure would be comet tails. Haley’s comet is shown in.

Halley’s Comet : As a comet approaches the inner Solar System, solar radiation causes the volatile materials within the comet to vaporize and stream out of the nucleus. The streams of dust and gas thus released form an atmosphere around the comet (called the coma), and the force exerted on the coma by the Sun’s radiation pressure and solar wind cause the formation of an enormous tail that points away from the Sun.

Although radiation pressure can be understood using classical electrodynamics, here we will examine the quantum mechanical argument. From the perspective of quantum theory, light is made of photons: particles with zero mass but which carry energy and – importantly in this argument – momentum. According to special relativity, because photons are devoid of mass, their energy (E) and momentum (p) are related by E=pc.

Now consider a beam of light perpendicularly incident on a surface, and let us assume the beam of light is totally absorbed. The momentum the photons carry is a conserved quantity (i.e., it cannot be destroyed) so it must be transferred to the surface; thus the absorption of the light beam causes the surface to gain momentum. Newton’s Second Law tells us that force equals rate of change of momentum; thus during each second, the surface experiences a force (or pressure, as pressure is force per unit area) due to the momentum the photons transfer to it.

This gives us: pressure = momentum transferred per second per unit area = energy deposited per second per unit area / c = I/c, (where I is the intensity of the beam of light).

Laser Cooling

There are many variations of laser cooling, but they all use radiation pressure to remove energy from atomic gases (and therefore cool the sample). In laser cooling (sometimes called Doppler cooling), the frequency of light is tuned slightly below an electronic transition in the atom. Because light is detuned to the “red” (i.e., at lower frequency) of the transition, the atoms will absorb more photons if they move towards the light source, due to the Doppler effect. Thus if one applies light from two opposite directions, the atoms will always scatter more photons from the laser beam pointing opposite to their direction of motion (typical setups applies three opposing pairs of laser beams as in ).

The Magneto Optical Trap : Experimental setup of Magneto Optical Trap (MOT), which uses radiation pressure to cool atomic species. Atoms are slowed down by absorbing (and emitting) photons.

In each scattering event, the atom loses a momentum equal to the momentum of the photon. If the atom (which is now in the excited state) then emits a photon spontaneously, it will be kicked by the same amount of momentum, only in a random direction. Since the initial momentum loss was opposite to the direction of motion (while the subsequent momentum gain was in a random direction), the overall result of the absorption and emission process is to reduce the speed of the atom. If the absorption and emission are repeated many times, the average speed (and therefore the kinetic energy ) of the atom will be reduced. Since the temperature of a group of atoms is a measure of the average random internal kinetic energy, this is equivalent to cooling the atoms. Simple laser cooling setups can produce a cold sample of atomic gases at around 1mK (=10 -3 K) starting from a room temperature gas.

• Maxwell’s four equations describe how electric charges and currents create electric and magnetic fields, and how they affect each other.
• Gauss’s law relates an electric field to the charge(s) that create(s) it.
• Gauss’s law for magnetism states that there are no “magnetic charges” analogous to electric charges, and that magnetic fields are instead generated by magnetic dipoles.
• Faraday’s law describes how a time-varying magnetic field (or flux ) induces an electric field. The principle behind this phenomenon is used in many electric generators.
• Ampere ‘s law originally stated that a magnetic field is created by an electrical current. Maxwell added that a changing electric flux can also generate a magnetic field.
• Electromagnetic waves consist of both electric and magnetic field waves. These waves oscillate in perpendicular planes with respect to each other, and are in phase.
• The creation of all electromagnetic waves begins with an oscillating charged particle, which creates oscillating electric and magnetic fields.
• Once in motion, the electric and magnetic fields that a charged particle creates are self-perpetuating: time-dependent changes in one field (electric or magnetic) produce the other.
• Max Planck proved that energy of a photon (a stream of which is an electromagnetic wave ) is quantized and can exist in multiples of “Planck’s constant” (denoted as h, approximately equal to 6.626×10 -34 J·s).
• \(\mathrm { E } = \mathrm { hf } = \frac { \mathrm { hc } } { \lambda } \)describes the energy (E) of a photon as a function of frequency (f), or wavelength (λ).
• \(\mathrm { p } = \frac { \mathrm { E } } { \mathrm { c } } = \frac { \mathrm { hf } } { \mathrm { c } } = \frac { \mathrm { h } } { \lambda }\) describes the momentum (p) of a photon as a function of its energy, frequency, or wavelength.
• The maximum possible value for the speed of light is that of light in a vacuum, and this speed is used for a constant in many area of physics.
• c is the symbol used to represent the speed of light in a vacuum, and its value is 299,792,458 meters per second.
• When light travels through medium, its speed is hindered by the index of refraction of that medium. Its actual speed can be found with: \(v=\frac{c}{n}\).
• The Doppler effect is very commonly observed in action.
• The Doppler effect can be observed in the apparent change in pitch of a siren on an emergency vehicle, according to a stationary observer.
• The observer will notice the Doppler effect on the pitch of the stationary siren when moving relative to its pitch, or if the medium moves when the observer is stationary.
• Photons carry momentum (p = E/c). When photons are absorbed or reflected on a surface, the surface receives momentum kicks. This momentum transfer leads to radiation pressure.
• Electromagnetic radiation applies radiation pressure equal to the Intensity (of light beam) divided by c (speed of light).
• Laser cooling uses radiation pressure to remove energy from atomic gases. The technique can produce cold samples of gases at 1mK or so.
• differential equation : An equation involving the derivatives of a function.
• flux : A quantitative description of the transfer of a given vector quantity through a surface. In this context, we refer to the electric flux and magnetic flux.
• electromagnetic wave : A wave of oscillating electric and magnetic fields.
• phase : Waves are said to be “in phase” when they begin at the same part (e.g., crest) of their respective cycles.
• photon : The quantum of light and other electromagnetic energy, regarded as a discrete particle having zero rest mass, no electric charge, and an indefinitely long lifetime.
• wavelength : The length of a single cycle of a wave, as measured by the distance between one peak or trough of a wave and the next; it is often designated in physics as λ, and corresponds to the velocity of the wave divided by its frequency.
• frequency : The quotient of the number of times n a periodic phenomenon occurs over the time t in which it occurs: f = n / t.
• special relativity : A theory that (neglecting the effects of gravity) reconciles the principle of relativity with the observation that the speed of light is constant in all frames of reference.
• refractive index : The ratio of the speed of light in air or vacuum to that in another medium.
• doppler effect : Apparent change in frequency of a wave when the observer and the source of the wave move relative to each other.
• classical electrodynamics : A branch of theoretical physics that studies consequences of the electromagnetic forces between electric charges and currents.

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What is the speed of light? Here’s the history, discovery of the cosmic speed limit

On one hand, the speed of light is just a number: 299,792,458 meters per second. And on the other, it’s one of the most important constants that appears in nature and defines the relationship of causality itself.

As far as we can measure, it is a constant. It is the same speed for every observer in the entire universe. This constancy was first established in the late 1800’s with the experiments of Albert Michelson and Edward Morley at Case Western Reserve University . They attempted to measure changes in the speed of light as the Earth orbited around the Sun. They found no such variation, and no experiment ever since then has either.

Observations of the cosmic microwave background, the light released when the universe was 380,000 years old, show that the speed of light hasn’t measurably changed in over 13.8 billion years.

In fact, we now define the speed of light to be a constant, with a precise speed of 299,792,458 meters per second. While it remains a remote possibility in deeply theoretical physics that light may not be a constant, for all known purposes it is a constant, so it’s better to just define it and move on with life.

How was the speed of light first measured?

In 1676 the Danish astronomer Ole Christensen Romer made the first quantitative measurement of how fast light travels. He carefully observed the orbit of Io, the innermost moon of Jupiter. As the Earth circles the Sun in its own orbit, sometimes it approaches Jupiter and sometimes it recedes away from it. When the Earth is approaching Jupiter, the path that light has to travel from Io is shorter than when the Earth is receding away from Jupiter. By carefully measuring the changes to Io’s orbital period, Romer calculated a speed of light of around 220,000 kilometers per second.

Observations continued to improve until by the 19 th century astronomers and physicists had developed the sophistication to get very close to the modern value. In 1865, James Clerk Maxwell made a remarkable discovery. He was investigating the properties of electricity and magnetism, which for decades had remained mysterious in unconnected laboratory experiments around the world. Maxwell found that electricity and magnetism were really two sides of the same coin, both manifestations of a single electromagnetic force.

As Maxwell explored the consequences of his new theory, he found that changing magnetic fields can lead to changing electric fields, which then lead to a new round of changing magnetic fields. The fields leapfrog over each other and can even travel through empty space. When Maxwell went to calculate the speed of these electromagnetic waves, he was surprised to see the speed of light pop out – the first theoretical calculation of this important number.

What is the most precise measurement of the speed of light?

Because it is defined to be a constant, there’s no need to measure it further. The number we’ve defined is it, with no uncertainty, no error bars. It’s done. But the speed of light is just that – a speed. The number we choose to represent it depends on the units we use: kilometers versus miles, seconds versus hours, and so on. In fact, physicists commonly just set the speed of light to be 1 to make their calculations easier. So instead of trying to measure the speed light travels, physicists turn to more precisely measuring other units, like the length of the meter or the duration of the second. In other words, the defined value of the speed of light is used to establish the length of other units like the meter.

How does light slow down?

Yes, the speed of light is always a constant. But it slows down whenever it travels through a medium like air or water. How does this work? There are a few different ways to present an answer to this question, depending on whether you prefer a particle-like picture or a wave-like picture.

In a particle-like picture, light is made of tiny little bullets called photons. All those photons always travel at the speed of light, but as light passes through a medium those photons get all tangled up, bouncing around among all the molecules of the medium. This slows down the overall propagation of light, because it takes more time for the group of photons to make it through.

In a wave-like picture, light is made of electromagnetic waves. When these waves pass through a medium, they get all the charged particles in motion, which in turn generate new electromagnetic waves of their own. These interfere with the original light, forcing it to slow down as it passes through.

Either way, light always travels at the same speed, but matter can interfere with its travel, making it slow down.

Why is the speed of light important?

The speed of light is important because it’s about way more than, well, the speed of light. In the early 1900’s Einstein realized just how special this speed is. The old physics, dominated by the work of Isaac Newton, said that the universe had a fixed reference frame from which we could measure all motion. This is why Michelson and Morley went looking for changes in the speed, because it should change depending on our point of view. But their experiments showed that the speed was always constant, so what gives?

Einstein decided to take this experiment at face value. He assumed that the speed of light is a true, fundamental constant. No matter where you are, no matter how fast you’re moving, you’ll always see the same speed.

This is wild to think about. If you’re traveling at 99% the speed of light and turn on a flashlight, the beam will race ahead of you at…exactly the speed of light, no more, no less. If you’re coming from the opposite direction, you’ll still also measure the exact same speed.

This constancy forms the basis of Einstein’s special theory of relativity, which tells us that while all motion is relative – different observers won’t always agree on the length of measurements or the duration of events – some things are truly universal, like the speed of light.

Can you go faster than light speed?

Nope. Nothing can. Any particle with zero mass must travel at light speed. But anything with mass (which is most of the universe) cannot. The problem is relativity. The faster you go, the more energy you have. But we know from Einstein’s relativity that energy and mass are the same thing. So the more energy you have, the more mass you have, which makes it harder for you to go even faster. You can get as close as you want to the speed of light, but to actually crack that barrier takes an infinite amount of energy. So don’t even try.

How is the speed at which light travels related to causality?

If you think you can find a cheat to get around the limitations of light speed, then I need to tell you about its role in special relativity. You see, it’s not just about light. It just so happens that light travels at this special speed, and it was the first thing we discovered to travel at this speed. So it could have had another name. Indeed, a better name for this speed might be “the speed of time.”

Related: Is time travel possible? An astrophysicist explains

We live in a universe of causes and effects. All effects are preceded by a cause, and all causes lead to effects. The speed of light limits how quickly causes can lead to effects. Because it’s a maximum speed limit for any motion or interaction, in a given amount of time there’s a limit to what I can influence. If I want to tap you on the shoulder and you’re right next to me, I can do it right away. But if you’re on the other side of the planet, I have to travel there first. The motion of me traveling to you is limited by the speed of light, so that sets how quickly I can tap you on the shoulder – the speed light travels dictates how quickly a single cause can create an effect.

The ability to go faster than light would allow effects to happen before their causes. In essence, time travel into the past would be possible with faster-than-light travel. Since we view time as the unbroken chain of causes and effects going from the past to the future, breaking the speed of light would break causality, which would seriously undermine our sense of the forward motion of time.

Why does light travel at this speed?

No clue. It appears to us as a fundamental constant of nature. We have no theory of physics that explains its existence or why it has the value that it does. We hope that a future understanding of nature will provide this explanation, but right now all investigations are purely theoretical. For now, we just have to take it as a given.

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Light Propagation Through a Medium

The mechanism by which a light wave is transported through a medium occurs in a manner that is similar to the way that any other wave is transported - by particle-to-particle interaction. In Unit 10 of The Physics Classroom Tutorial , the particle-to-particle interaction mechanism by which a mechanical wave transports energy was discussed in detail. In Unit 12 of The Physics Classroom Tutorial , the mechanism of energy transport by an electromagnetic wave was briefly discussed. Here we will look at this method in more detail.

An electromagnetic wave (i.e., a light wave) is produced by a vibrating electric charge. As the wave moves through the vacuum of empty space, it travels at a speed of c (3 x 10 8 m/s). This value is the speed of light in a vacuum. When the wave impinges upon a particle of matter, the energy is absorbed and sets electrons within the atoms into vibrational motion. If the frequency of the electromagnetic wave does not match the resonant frequency of vibration of the electron , then the energy is reemitted in the form of an electromagnetic wave. This new electromagnetic wave has the same frequency as the original wave and it too will travel at a speed of c through the empty space between atoms. The newly emitted light wave continues to move through the interatomic space until it impinges upon a neighboring particle. The energy is absorbed by this new particle and sets the electrons of its atoms into vibration motion. And once more, if there is no match between the frequency of the electromagnetic wave and the resonant frequency of the electron, the energy is reemitted in the form of a new electromagnetic wave. The cycle of absorption and reemission continues as the energy is transported from particle to particle through the bulk of a medium. Every photon (bundle of electromagnetic energy) travels between the interatomic void at a speed of c ; yet time delay involved in the process of being absorbed and reemitted by the atoms of the material lowers the net speed of transport from one end of the medium to the other. Subsequently, the net speed of an electromagnetic wave in any medium is somewhat less than its speed in a vacuum - c (3 x 10 8 m/s).

Optical Density and the Index of Refraction

Like any wave, the speed of a light wave is dependent upon the properties of the medium. In the case of an electromagnetic wave, the speed of the wave depends upon the optical density of that material. The optical density of a medium is not the same as its physical density. The physical density of a material refers to the mass/volume ratio. The optical density of a material relates to the sluggish tendency of the atoms of a material to maintain the absorbed energy of an electromagnetic wave in the form of vibrating electrons before reemitting it as a new electromagnetic disturbance. The more optically dense that a material is, the slower that a wave will move through the material.

One indicator of the optical density of a material is the index of refraction value of the material. Index of refraction values (represented by the symbol n ) are numerical index values that are expressed relative to the speed of light in a vacuum. The index of refraction value of a material is a number that indicates the number of times slower that a light wave would be in that material than it is in a vacuum. A vacuum is given an n value of 1.0000. The n values of other materials are found from the following equation:

The table below lists index of refraction values for a variety of medium. The materials listed at the top of the table are those through which light travels fastest; these are the least optically dense materials. The materials listed at the bottom of the table are those through which light travels slowest; these are the most optically dense materials. So as the index of refraction value increases, the optical density increases, and the speed of light in that material decreases.

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Look it up.

The index of refraction values provide a measure of the relative speed of a light wave in a particular medium. Knowledge of such relative speeds allows a student of physics to predict which way a light ray would bend when passing from one medium to another. In the next part of Lesson 1 , the rules for the direction of bending will be discussed in detail.

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Refraction of Light

Learn about the refraction of light and Snell's law. Learn how to solve for the angle that light bends when going from one medium to another.

The reason why a pencil in water appears to be bending is due to the speed of light in different medium.  Light bends when approaching a boundary between to medium where the speed of light is different.  Light travels faster in air and slower in water creating the phenomenon you see here.

Refraction of Light Variables

The speed of light in various medium.

Light is an electromagnetic wave that travels fastest in the vacuum of space, slower in gas, and slowest in a solid because of density.

• Review our other lesson about speed of an electromagnetic wave and density following this link.

Light has a different speed in different translucent solids.  Translucent means you can see through them.  The velocity that light will travel in a certain medium can be calculated using a variable called the index of refraction ( n ).  This will also be used later on this page to determine how much light will bend from one medium to another.

Index of Refraction (n)

The index of refraction is the ratio of speed of light in a vacuum ( c ) to speed of light in another medium ( v ).

• The index of refraction (n) is always 1 or greater
• The larger the index of refraction (n) the slower light travels in that medium
• The index of refraction (n) has as no unit

The variable c is a constant that stands for the speed of light in a vacuum.  This is the universal speed limit and always 3.0 x 10 8 m/s with nothing faster.

The index of refraction equation is:

Variables in this equation are:

c = 3.0 x 10 8 m/s

n = index of refraction

v = velocity of light in a medium

Since c is a constant 3.0 x 10 8 m/s, the index of refraction equation n = c/v will always be n = (3.0 x 10 8 )/v

The index of refraction (n) will never be less than 1 since the velocity of light in any medium (v) can not be faster than the universal speed limit (c) of 3.0 x 10 8 m/s.  The denominator of n =c/ v  will never be bigger than the numerator and therefore not give an index of refraction (n) below 1.

Example Problems

1. What is the speed of light in water that has an index of refraction of 1.333?

rearranges to v = c/n

v = (3.0 x 10 8 )/(1.333) =

225056264.1 m/s

rounded in scientific notation becomes

v = 2.25 x 10 8 m/s

2. What is the speed of light in diamond that has an index of refraction of 2.419?

v = (3.0 x 10 8 )/(2.419) =

124018189.3 m/s

v = 1.24 x 10 8 m/s

3. What is the index of refraction for ice at 20° C where light travels at 2.29 x 10 8 m/s?

v = 2.29 x 10 8 m/s

n = (3.0 x 10 8 )/(2.29 x 10 8 ) =

4. Does light travel faster in diamond with an index of refraction of 2.419 or cubic zirconia with an index of refraction of 2.20?

The larger the index of refraction (n) the slower light is traveling in the medium.

Refraction of Light Into New Medium

Light changing speed in a new medium creates a bending.

• If light is traveling slower in the new medium it will bend towards the normal line
• If light is traveling faster in the new medium it will bend away from the normal line

Slower Medium to Faster Medium

Observe that as light enters the right side of the diagram it has a smaller index of refraction (n r ) which means it is traveling faster.  Light bends away from the normal line on the second or refracted side when this happens.

• Slower medium to faster medium
• (n i ) bigger than (n r )
• Bends away from the normal line

Faster Medium to Slower Medium

Observe that as light enters the right side of the diagram it has a larger index of refraction (n r ) which means it is traveling slower.  Light bends towards the normal line on the second or refracted side when this happens.

• Faster medium to slower medium
• (n i ) smaller than (n r )
• Bends toward the normal line

Snell's Law

Snell's law can be used to mathematically calculate the angle of bend or index of refraction on the incident side or refracted side when light travels between two medium.

With two medium we need subscripts to specify the side light is traveling in.  Use subscripts (i) for incident side and (r) for refracted side.

• Incident (i) : first side where light starts
• Refracted(r) : second side where light goes

(n i )(sin Ө i ) = (n r )(sin Ө r )

N i = index of refraction on the incident side, ө i = angle of refraction on the incident side, n r = index of refraction on the refracted side, ө r = angle of refraction on the refracted side.

Calculation Tips With Snell's Law

You will have to do a bit of algebra to solve for various components in Snell's law.  Here are the rearranged equations you can check your work with.

• When using Sin and Sin -1 you will have to make sure your calculator’s mode is in degrees .  With most TI graphing calculators there is a button for mode.  When you hit mode, there is an option for radian or degree.  Make sure it is on degrees.  This may be a reason if you do everything right but your calculated answer is wrong.
• Be sure to use the correct trig function Sin or Sin -1 if you are not getting the right answer this may also be why.
• Use lots of (parenthesis) , your calculator follows the order of operations and this makes sure the entire value you are calculating is in the right place

5. Will light bend toward or away from the normal line when going from a slow medium to a fast medium?

Away form the normal line

6. Will light bend toward or away from the normal line when going from air (n=1.00) to water (n=1.33)?

Towards the normal line.

n i = smaller so faster

n r = bigger so slower

7. What is the angle of refraction when the angle of incidence is 20° when going from air (n=1.00) to water (n=1.33)?

8. What is the angle of incidence when the angle of refraction is 15 ° when going from diamond (n=2.42) to water (n=1.33)?

9. What is the index of refraction for an unknown substance when the angle of incidence is 20° in air (n=1.00) and angle of refraction is 15° in the unknown substance?

10. What is the index of refraction for an unknown substance when the angle of incidence is 31 ° in the unknown and a angle of refraction is 26° in water (n=1.33) ?

Total Internal Reflection

Light bends away from the normal line when going from a slower to a faster medium.  As the angle of incidence increases, so does the angle of refraction.  Light no longer refracts into a faster medium after a certain angle called the critical angle.  Beyond the critical angle you have total internal reflection and no refraction.

Solving for the critical angle (Ө c ):

Ө c = sin -1 ((n r )/ (n i ))

• Total Internal Reflection : After passing the critical angle, light no longer refracts only reflects
• Critical Angle : Angle of incidence after which light will only reflect and not refract
• You will only have a critical angle and total internal reflection when light travels from slow to fast medium where light bends away from the normal line.

Example Problem

11. What is the critical angle for light in diamond (2.42) going into to air (1.00)?

Click Here For the PhET Snell's Law Mini Lab Lab sheet And Walkthrough

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How does light slow down?

Slowing down light is not as easy as it sounds.

The phenomenon of light slowing down as it passes through a material like glass or air is one of the most fascinating areas of physics, involving a complex interaction between light and materials. There are three ways to look at the same situation, and each employs a different understanding of physics. 

All of these explanations have strengths and weaknesses, but all of them are powerful tools for understanding this fascinating interaction.

  Related: How does astronomy use the electromagnetic spectrum?  

View No. 1: It's all waves 

The first perspective comes from James Clerk Maxwell , the 19th-century Scottish physicist and all-around genius who discovered a unified theory of electricity and magnetism, and also found that light is made of waves of electricity and magnetism.

 When these waves encounter a material like glass or water, they see a whole bunch of charged particles. The molecules in the material are made of atoms , which have protons and electrons — both charged particles. And charged particles respond to electromagnetic waves passing by them by wiggling along with them.

But moving charged particles also create electromagnetic waves of their own. The result is a giant mess, with the original electromagnetic waves interfering with all the waves generated by all the charged particles in the material (and there are a lot). Thankfully, most of those waves, except the waves traveling in the original direction of the light, cancel each other out. But because the waves generated by the particles are a little delayed, the entire ensemble moves more slowly.

The end result: The light moves more slowly.

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View No. 2: It's all particles 

Maxwell's theory is a classical picture of radiation. Nowadays, we have a much more sophisticated view based on quantum mechanics, where light is made of countless tiny particles known as photons. Photons can act individually, but when enough of them get together, they display all of the same properties as electromagnetic waves.

A fully quantum treatment of photons interacting with materials can get pretty nasty, but thankfully, we have an approach developed by the famed physicist Richard Feynman to guide us through it. We can imagine all the photons of the incoming light slamming into the material. Once inside, they begin interacting with all the charged particles. 

— Why is the speed of light the way it is?

— The double-slit experiment: Is light a wave or a particle?

— 10 mind-boggling things you should know about quantum physics  

Those charged particles can absorb those photons and emit their own, because that's what charged particles do. But these photons are a little different. In physics, they're known as virtual photons. 

Remember that photons can do two things: They can roam freely through the universe , existing as independent entities (this is light), and they do the legwork of mediating the electromagnetic force (like the force holding a magnet to a fridge). But these photons don't roam freely; they have a job to do. So we call them "virtual" photons — they exist only in our math to help us account for the electromagnetic force.

So all of these charged particles start emitting copious amounts of virtual particles, and once again, there's a giant, confusing mess. Feynman came to the rescue. He developed a technique of averaging out all of the possible paths that those photons can take. That averaging process eliminated all the wayward photons, leaving behind only the ones traveling in the original direction of the light. But all of those interactions come at a cost: It takes time for an electron to absorb and reemit a photon, and those delays add up.

View No. 3: It's all polaritons 

So far, we've focused on the properties of light, viewing it through a particle-based lens and a wave-based lens. But the material is more than a simple collection of charged particles that just do whatever they are electromagnetically ordered to do.

Materials can be interesting, too. Specifically, all materials can support vibrations — little ones, big ones, ones that last a long time, ones that fade away quickly. All material is constantly in motion, and that motion affects how that material interacts with everything else. To help physicists grapple with the complexities of all the kinds of vibrations that are constantly racing through materials, they proposed an entity known as a phonon.

A phonon is another kind of fake particle, but like virtual photons, it's very useful. It allows physicists to use the language of quantum mechanics to describe the vibrations in a material. This new language comes in handy when light, which is made of photons, enters that material.

When photons and phonons get together, they create something new: a polariton. In this view, when light enters a material, it disappears. And so do the phonons in the material itself. Instead, they get replaced by polaritons. These polaritons share a lot of properties with their parents, but they have one crucial property: They travel more slowly than the speed of light .

That speed depends on the properties of the material (the phonons). In this view, it's not light that's passing through a material, with the material responding to it, but a new object, a polariton, passing through. This view is especially useful, because in many situations, it's very easy to discard all the cumbersome math of conflicting waves or bouncing photons and just deal with a straightforward, simple entity that already encodes all the information you need.

Light goes in, a polariton travels through and light goes out.

Learn more by listening to the "Ask A Spaceman" podcast, available on iTunes and askaspaceman.com . Ask your own question on Twitter using #AskASpaceman or by following Paul @PaulMattSutter and facebook.com/PaulMattSutter .

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Paul M. Sutter is an astrophysicist at SUNY Stony Brook and the Flatiron Institute in New York City. Paul received his PhD in Physics from the University of Illinois at Urbana-Champaign in 2011, and spent three years at the Paris Institute of Astrophysics, followed by a research fellowship in Trieste, Italy, His research focuses on many diverse topics, from the emptiest regions of the universe to the earliest moments of the Big Bang to the hunt for the first stars. As an "Agent to the Stars," Paul has passionately engaged the public in science outreach for several years. He is the host of the popular "Ask a Spaceman!" podcast, author of "Your Place in the Universe" and "How to Die in Space" and he frequently appears on TV — including on The Weather Channel, for which he serves as Official Space Specialist.

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• Atlan0001 Then you have the classical, SPACETIME, otherwise also known as LIGHT -TIME or simply "histories"! In closed system, the ceiling horizon fastest speed there is! In open system, the floor horizon slowest speed there is! An objective real in space and time will always be out front in space and time of the SPACETIME ( LIGHT -TIME) subjective relative. Going away from anywhere in SPACE and TIME, the objective real, and therefore its clock, will be farther out front, to ever far farther out front, in space and time from anywhere than its SPACETIME ( LIGHT -TIME) subjective relative hologram. Oncoming to anywhere in SPACE and TIME, the objective real, and therefore its clock, will still be farther out front, to far farther out front, in space and time, than its SPACETIME ( LIGHT -TIME) subjective relative hologram gradually speeding up in SPACETIME (in LIGHT -TIME) in closing upon the objectively real, itself closing upon points of objective reality anywhere at all. The triangle of three points (including the subjectively relative hologram and its subjectively relative clock and clock time) will close at the 0-point closure of the two objective reals . . . including the two objectively real clocks and their objectively real clocked times. A SPACETIME ( LIGHT -TIME) holographic constant of speed that slows down in objective expansions going away from object points anywhere and everywhere . . . and equally but oppositely speeds up in objective contractions oncoming to object points anywhere and everywhere. But always until the very last instant of time, and then only in oncoming to the closing of objectively real points, so slow (in any open or opening system whatsoever) as to be unable to catch up to any objective real in SPACE and TIME until the meeting point of objective reals. An amazing thing to be universally the fastest speed there is in a closed or closing system yet universally be the slowest speed in any open or opening system . . . to be nothing -- both slowing down going away and speeding up oncoming -- but future-past // past-future "'histories' on the clock!" Reply
• 24launch What I'm curious about then is why does light bend or refract when passing through these materials? These 3 explanations for why it slows down don't address that phenomenon. I do have QED, by Richard Feynman and while I've made several attempts to read it, just didn't get terribly far. I'm betting he addresses it. Reply

24launch said: What I'm curious about then is why does light bend or refract when passing through these materials? These 3 explanations for why it slows down don't address that phenomenon. I do have QED, by Richard Feynman and while I've made several attempts to read it, just didn't get terribly far. I'm betting he addresses it.

• sNarayana Light slows down when it enters a medium, like glass. This is what is explained in this article. When the light leaves the glass medium and enters air (or, vacuum) it regains its original speed. Please explain that. Reply
• billslugg The speed of light never changes. In the refractive medium, the light stops for a moment at each atom and pays a short visit. In between atoms it is at the usual speed. Reply
• Classical Motion I think it spins. And the spin motion is taken from the c motion. And added back to it when the light leaves and stops spinning. It doesn't really slow down, but has a longer path, because of the twist. Mass spins it. Different F, angle input...... rates and separates the spins. A prism. A normal angle can rate equal spins for many F. A pane. Reply
• billslugg Single photons reflect, refract and interfere just a collections of photons do. Single photons fired one at a time at a lens will act just the same. In fact, even solid particles will show a diffraction pattern through a slit when fired one at a time. Reply

billslugg said: Single photons reflect, refract and interfere just a collections of photons do. Single photons fired one at a time at a lens will act just the same. In fact, even solid particles will show a diffraction pattern through a slit when fired one at a time.

• billslugg Yes, a single photon will follow the same path multiple photons do. It has both wave and particle characteristics. It is the wave function dominates in the transit of a medium. This "same path" applies to reflection, refraction and diffraction. It applies to waves and particles. Reply
• View All 11 Comments

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Understanding the Speed of Electromagnetic Waves

Learn Science

Electromagnetic waves are a fundamental aspect of physics and play a crucial role in various fields, including telecommunications, astronomy, and medical imaging. These waves are responsible for the transmission of energy in the form of electric and magnetic fields. Understanding the speed at which these waves propagate is essential for comprehending their behavior and applications. In this article, we will delve into the concept of wave propagation, explore the speed of electromagnetic waves across the electromagnetic spectrum, and discuss the energy spectrum associated with these waves. We will also touch upon the implications of these concepts in real-world applications and scientific research.

Wave Propagation

Wave propagation refers to the movement of waves through a medium or space. This is a fundamental concept in physics that applies to all types of waves, including sound waves, water waves, and of course, electromagnetic waves. In the case of electromagnetic waves, they can propagate through a vacuum, such as outer space, or through a medium, such as air or water. The speed at which electromagnetic waves propagate depends on the properties of the medium through which they travel. For instance, electromagnetic waves travel slower in denser media due to the increased interaction with the particles in the medium.

Speed of Electromagnetic Waves

The speed of electromagnetic waves in a vacuum is a constant value denoted by the symbol “c.” This value is approximately 299,792,458 meters per second, which is equivalent to the speed of light. The speed of light is a fundamental constant in physics and serves as a universal speed limit. No object or information can travel faster than the speed of light in a vacuum. This concept, which is a cornerstone of Einstein’s theory of relativity, has profound implications for our understanding of space, time, and the nature of the universe.

Electromagnetic Spectrum Speed

The electromagnetic spectrum encompasses a wide range of electromagnetic waves, each with its own unique properties and applications. The speed at which electromagnetic waves propagate varies across the spectrum, but it is important to note that all electromagnetic waves travel at the speed of light in a vacuum, regardless of their frequency or wavelength.

At the lower end of the spectrum, we have radio waves. These waves have the longest wavelength and the lowest frequency. Radio waves can travel at the speed of light, just like all other electromagnetic waves. This means that radio waves also travel at approximately 299,792,458 meters per second in a vacuum. Radio waves are used in various applications, including broadcasting, radar, and satellite communication.

Moving up the spectrum, we encounter microwaves. Microwaves have shorter wavelengths and higher frequencies compared to radio waves. The speed at which microwaves propagate is also the same as the speed of light. Microwaves are used in a variety of applications, including cooking, telecommunications, and radar systems.

Next, we have infrared waves. Infrared waves have even shorter wavelengths and higher frequencies than microwaves. Again, the speed at which infrared waves propagate is equal to the speed of light. Infrared waves are used in a variety of applications, including thermal imaging, remote controls, and fiber-optic communications.

Continuing up the spectrum, we reach the visible light region. Visible light consists of different colors, each with its own wavelength and frequency. Despite the variation in wavelength and frequency, all colors of visible light travel at the same speed, which is the speed of light. Visible light is, of course, essential for vision, but it also has numerous other applications, including photography, illumination, and optical communication.

Moving further up the spectrum, we encounter ultraviolet waves. Ultraviolet waves have shorter wavelengths and higher frequencies than visible light. Similar to the previous waves, the speed at which ultraviolet waves propagate is equal to the speed of light. Ultraviolet waves are used in a variety of applications, including sterilization, air purification, and the production of vitamin D in the skin.

Next, we have X-rays. X-rays have even shorter wavelengths and higher frequencies compared to ultraviolet waves. Once again, the speed at which X-rays propagate is the same as the speed of light. X-rays are used in a variety of applications, including medical imaging, material analysis, and airport security.

Finally, at the highest end of the spectrum, we have gamma rays. Gamma rays have the shortest wavelengths and the highest frequencies of all electromagnetic waves. Just like all other electromagnetic waves, gamma rays also travel at the speed of light. Gamma rays are used in a variety of applications, including medical treatments, sterilization, and astronomical observations.

Energy Spectrum

The energy of electromagnetic waves is directly proportional to their frequency. This means that waves with higher frequencies have higher energy levels. As we move up the electromagnetic spectrum, the frequency and energy of the waves increase. This relationship between energy and frequency is described by Planck’s equation, which states that the energy of a wave is equal to its frequency multiplied by Planck’s constant.

Radio waves, at the lower end of the spectrum, have the lowest energy levels. Microwaves have slightly higher energy levels than radio waves, followed by infrared waves, visible light, ultraviolet waves, X-rays, and gamma rays, which have the highest energy levels.

The energy spectrum of electromagnetic waves is crucial in various applications. For example, in medical imaging, X-rays are used due to their ability to penetrate tissues and create detailed images of bones and internal organs. Gamma rays, on the other hand, are used in radiation therapy to treat cancer due to their high energy levels. The energy of electromagnetic waves is also crucial in telecommunications, as it determines the amount of information that can be transmitted and the distance over which it can be transmitted.

Understanding the speed of electromagnetic waves is essential for comprehending their behavior and applications. The speed of electromagnetic waves in a vacuum is a constant value known as the speed of light. This speed serves as a universal speed limit. The speed at which electromagnetic waves propagate varies across the electromagnetic spectrum, with all waves traveling at the speed of light. Additionally, the energy of electromagnetic waves increases as we move up the spectrum, with gamma rays having the highest energy levels. By understanding these concepts, we can better appreciate the role of electromagnetic waves in our everyday lives and various scientific fields. This knowledge is not only fascinating in its own right, but it also has practical implications for technology, medicine, and our understanding of the universe.

Wave Behaviors

Light waves across the electromagnetic spectrum behave in similar ways. When a light wave encounters an object, they are either transmitted, reflected, absorbed, refracted, polarized, diffracted, or scattered depending on the composition of the object and the wavelength of the light.

Specialized instruments onboard NASA spacecraft and airplanes collect data on how electromagnetic waves behave when they interact with matter. These data can reveal the physical and chemical composition of matter.

Reflection is when incident light (incoming light) hits an object and bounces off. Very smooth surfaces such as mirrors reflect almost all incident light.

The color of an object is actually the wavelengths of the light reflected while all other wavelengths are absorbed. Color, in this case, refers to the different wavelengths of light in the visible light spectrum perceived by our eyes. The physical and chemical composition of matter determines which wavelength (or color) is reflected.

This reflective behavior of light is used by lasers onboard NASA's Lunar Reconnaissance Orbiter to map the surface of the Moon. The instrument measures the time it takes a laser pulse to hit the surface and return. The longer the response time, the farther away the surface and lower the elevation. A shorter response time means the surface is closer or higher in elevation. In this image of the Moon's southern hemisphere, low elevations are shown as purple and blue, and high elevations are shown in red and brown.

Absorption occurs when photons from incident light hit atoms and molecules and cause them to vibrate. The more an object's molecules move and vibrate, the hotter it becomes. This heat is then emitted from the object as thermal energy.

Some objects, such as darker colored objects, absorb more incident light energy than others. For example, black pavement absorbs most visible and UV energy and reflects very little, while a light-colored concrete sidewalk reflects more energy than it absorbs. Thus, the black pavement is hotter than the sidewalk on a hot summer day. Photons bounce around during this absorption process and lose bits of energy to numerous molecules along the way. This thermal energy then radiates in the form of longer wavelength infrared energy.

Thermal radiation from the energy-absorbing asphalt and roofs in a city can raise its surface temperature by as much as 10° Celsius. The Landsat 7 satellite image below shows the city of Atlanta as an island of heat compared to the surrounding area. Sometimes this warming of air above cities can influence weather, which is called the "urban heat island" effect.

Diffraction

Diffraction is the bending and spreading of waves around an obstacle. It is most pronounced when a light wave strikes an object with a size comparable to its own wavelength. An instrument called a spectrometer uses diffraction to separate light into a range of wavelengths—a spectrum. In the case of visible light, the separation of wavelengths through diffraction results in a rainbow.

A spectrometer uses diffraction (and the subsequent interference) of light from slits or gratings to separate wavelengths. Faint peaks of energy at specific wavelengths can then be detected and recorded. A graph of these data is called a spectral signature. Patterns in a spectral signature help scientists identify the physical condition and composition of stellar and interstellar matter.

The graph below from the SPIRE infrared spectrometer onboard the ESA (European Space Agency) Herschel space telescope reveals strong emission lines from carbon monoxide (CO), atomic carbon, and ionized nitrogen in Galaxy M82.

Scattering occurs when light bounces off an object in a variety of directions. The amount of scattering that takes place depends on the wavelength of the light and the size and structure of the object.

The sky appears blue because of this scattering behavior. Light at shorter wavelengths—blue and violet—is scattered by nitrogen and oxygen as it passes through the atmosphere. Longer wavelengths of light—red and yellow—transmit through the atmosphere. This scattering of light at shorter wavelengths illuminates the skies with light from the blue and violet end of the visible spectrum. Even though violet is scattered more than blue, the sky looks blue to us because our eyes are more sensitive to blue light.

Aerosols in the atmosphere can also scatter light. NASA's Cloud-Aerosol Lidar and Infrared Pathfinder Satellite Observation (CALIPSO) satellite can observe the scattering of laser pulses to "see" the distributions of aerosols from sources such as dust storms and forest fires. The image below shows a volcanic ash cloud drifting over Europe from an eruption of Iceland's Eyjafjallajökull Volcano in 2010.

Refraction is when light waves change direction as they pass from one medium to another. Light travels slower in air than in a vacuum, and even slower in water. As light travels into a different medium, the change in speed bends the light. Different wavelengths of light are slowed at different rates, which causes them to bend at different angles.

Next: Visualization: From Energy to Image

National Aeronautics and Space Administration, Science Mission Directorate. (2010). Wave Behaviors. Retrieved [insert date - e.g. August 10, 2016] , from NASA Science website: http://science.nasa.gov/ems/03_behaviors

Science Mission Directorate. "Wave Behaviors" NASA Science . 2010. National Aeronautics and Space Administration. [insert date - e.g. 10 Aug. 2016] http://science.nasa.gov/ems/03_behaviors

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13.1 Types of Waves

Section learning objectives.

By the end of this section, you will be able to do the following:

• Define mechanical waves and medium, and relate the two
• Distinguish a pulse wave from a periodic wave
• Distinguish a longitudinal wave from a transverse wave and give examples of such waves

Teacher Support

The learning objectives in this section will help your students master the following standards:

• (A) examine and describe oscillatory motion and wave propagation in various types of media.

Section Key Terms

Mechanical waves.

What do we mean when we say something is a wave? A wave is a disturbance that travels or propagates from the place where it was created. Waves transfer energy from one place to another, but they do not necessarily transfer any mass. Light, sound, and waves in the ocean are common examples of waves. Sound and water waves are mechanical waves ; meaning, they require a medium to travel through. The medium may be a solid, a liquid, or a gas, and the speed of the wave depends on the material properties of the medium through which it is traveling. However, light is not a mechanical wave; it can travel through a vacuum such as the empty parts of outer space.

A familiar wave that you can easily imagine is the water wave. For water waves, the disturbance is in the surface of the water, an example of which is the disturbance created by a rock thrown into a pond or by a swimmer splashing the water surface repeatedly. For sound waves, the disturbance is caused by a change in air pressure, an example of which is when the oscillating cone inside a speaker creates a disturbance. For earthquakes, there are several types of disturbances, which include the disturbance of Earth’s surface itself and the pressure disturbances under the surface. Even radio waves are most easily understood using an analogy with water waves. Because water waves are common and visible, visualizing water waves may help you in studying other types of waves, especially those that are not visible.

Water waves have characteristics common to all waves, such as amplitude , period , frequency , and energy , which we will discuss in the next section.

Misconception Alert

Many people think that water waves push water from one direction to another. In reality, however, the particles of water tend to stay in one location only, except for moving up and down due to the energy in the wave. The energy moves forward through the water, but the water particles stay in one place. If you feel yourself being pushed in an ocean, what you feel is the energy of the wave, not the rush of water. If you put a cork in water that has waves, you will see that the water mostly moves it up and down.

[BL] [OL] [AL] Ask students to give examples of mechanical and nonmechanical waves.

Pulse Waves and Periodic Waves

If you drop a pebble into the water, only a few waves may be generated before the disturbance dies down, whereas in a wave pool, the waves are continuous. A pulse wave is a sudden disturbance in which only one wave or a few waves are generated, such as in the example of the pebble. Thunder and explosions also create pulse waves. A periodic wave repeats the same oscillation for several cycles, such as in the case of the wave pool, and is associated with simple harmonic motion. Each particle in the medium experiences simple harmonic motion in periodic waves by moving back and forth periodically through the same positions.

[BL] Any kind of wave, whether mechanical or nonmechanical, or transverse or longitudinal, can be in the form of a pulse wave or a periodic wave.

Consider the simplified water wave in Figure 13.2 . This wave is an up-and-down disturbance of the water surface, characterized by a sine wave pattern. The uppermost position is called the crest and the lowest is the trough . It causes a seagull to move up and down in simple harmonic motion as the wave crests and troughs pass under the bird.

Longitudinal Waves and Transverse Waves

Mechanical waves are categorized by their type of motion and fall into any of two categories: transverse or longitudinal. Note that both transverse and longitudinal waves can be periodic. A transverse wave propagates so that the disturbance is perpendicular to the direction of propagation. An example of a transverse wave is shown in Figure 13.3 , where a woman moves a toy spring up and down, generating waves that propagate away from herself in the horizontal direction while disturbing the toy spring in the vertical direction.

In contrast, in a longitudinal wave , the disturbance is parallel to the direction of propagation. Figure 13.4 shows an example of a longitudinal wave, where the woman now creates a disturbance in the horizontal direction—which is the same direction as the wave propagation—by stretching and then compressing the toy spring.

Tips For Success

Longitudinal waves are sometimes called compression waves or compressional waves , and transverse waves are sometimes called shear waves .

Teacher Demonstration

Transverse and longitudinal waves may be demonstrated in the class using a spring or a toy spring, as shown in the figures.

Waves may be transverse, longitudinal, or a combination of the two . The waves on the strings of musical instruments are transverse (as shown in Figure 13.5 ), and so are electromagnetic waves, such as visible light. Sound waves in air and water are longitudinal. Their disturbances are periodic variations in pressure that are transmitted in fluids.

Sound in solids can be both longitudinal and transverse. Essentially, water waves are also a combination of transverse and longitudinal components, although the simplified water wave illustrated in Figure 13.2 does not show the longitudinal motion of the bird.

Earthquake waves under Earth’s surface have both longitudinal and transverse components as well. The longitudinal waves in an earthquake are called pressure or P-waves, and the transverse waves are called shear or S-waves. These components have important individual characteristics; for example, they propagate at different speeds. Earthquakes also have surface waves that are similar to surface waves on water.

Energy propagates differently in transverse and longitudinal waves. It is important to know the type of the wave in which energy is propagating to understand how it may affect the materials around it.

Watch Physics

Introduction to waves.

This video explains wave propagation in terms of momentum using an example of a wave moving along a rope. It also covers the differences between transverse and longitudinal waves, and between pulse and periodic waves.

• After a compression wave, some molecules move forward temporarily.
• After a compression wave, some molecules move backward temporarily.
• After a compression wave, some molecules move upward temporarily.
• After a compression wave, some molecules move downward temporarily.

Fun In Physics

The physics of surfing.

Many people enjoy surfing in the ocean. For some surfers, the bigger the wave, the better. In one area off the coast of central California, waves can reach heights of up to 50 feet in certain times of the year ( Figure 13.6 ).

How do waves reach such extreme heights? Other than unusual causes, such as when earthquakes produce tsunami waves, most huge waves are caused simply by interactions between the wind and the surface of the water. The wind pushes up against the surface of the water and transfers energy to the water in the process. The stronger the wind, the more energy transferred. As waves start to form, a larger surface area becomes in contact with the wind, and even more energy is transferred from the wind to the water, thus creating higher waves. Intense storms create the fastest winds, kicking up massive waves that travel out from the origin of the storm. Longer-lasting storms and those storms that affect a larger area of the ocean create the biggest waves since they transfer more energy. The cycle of the tides from the Moon’s gravitational pull also plays a small role in creating waves.

Actual ocean waves are more complicated than the idealized model of the simple transverse wave with a perfect sinusoidal shape. Ocean waves are examples of orbital progressive waves , where water particles at the surface follow a circular path from the crest to the trough of the passing wave, then cycle back again to their original position. This cycle repeats with each passing wave.

As waves reach shore, the water depth decreases and the energy of the wave is compressed into a smaller volume. This creates higher waves—an effect known as shoaling .

Since the water particles along the surface move from the crest to the trough, surfers hitch a ride on the cascading water, gliding along the surface. If ocean waves work exactly like the idealized transverse waves, surfing would be much less exciting as it would simply involve standing on a board that bobs up and down in place, just like the seagull in the previous figure.

Additional information and illustrations about the scientific principles behind surfing can be found in the “Using Science to Surf Better!” video.

• The surfer would move side-to-side/back-and-forth vertically with no horizontal motion.
• The surfer would forward and backward horizontally with no vertical motion.

Check Your Understanding

Use these questions to assess students’ achievement of the section’s Learning Objectives. If students are struggling with a specific objective, these questions will help identify such objective and direct them to the relevant content.

• A wave is a force that propagates from the place where it was created.
• A wave is a disturbance that propagates from the place where it was created.
• A wave is matter that provides volume to an object.
• A wave is matter that provides mass to an object.
• No, electromagnetic waves do not require any medium to propagate.
• No, mechanical waves do not require any medium to propagate.
• Yes, both mechanical and electromagnetic waves require a medium to propagate.
• Yes, all transverse waves require a medium to travel.
• A pulse wave is a sudden disturbance with only one wave generated.
• A pulse wave is a sudden disturbance with only one or a few waves generated.
• A pulse wave is a gradual disturbance with only one or a few waves generated.
• A pulse wave is a gradual disturbance with only one wave generated.

What are the categories of mechanical waves based on the type of motion?

• Both transverse and longitudinal waves
• Only longitudinal waves
• Only transverse waves
• Only surface waves

In which direction do the particles of the medium oscillate in a transverse wave?

• Perpendicular to the direction of propagation of the transverse wave
• Parallel to the direction of propagation of the transverse wave

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• Book title: Physics
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• Book URL: https://openstax.org/books/physics/pages/1-introduction
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Middle school physics - NGSS

Course: middle school physics - ngss   >   unit 4, mechanical waves and light.

• Understand: mechanical waves and light

Key points:

• Sound waves, water waves, and seismic waves are all types of mechanical waves.
• Light is a form of electromagnetic wave.
• A light wave’s amplitude determines how intense, or bright, it is. Its frequency determines the light wave’s color.
• A sound wave’s amplitude determines how loud it is. Its frequency determines the sound wave’s pitch.

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An electromagnetic wave travels in a medium with the speed of 2 × 10 8 m / s . The relative permeability of the medium is 1 . Find the relative permittivity of the medium.

Step 1: given data speed of light, c = 3 × 10 8 m / s speed of wave in the medium, v = 2 × 10 8 m / s relative permeability, μ r = 1 to find the relative permittivity of the medium. step 2: calculate relative permittivity( ε r ) using the formula: ε r = c 2 v 2 μ r = 3 × 10 8 2 2 × 10 8 2 × 1 = 2 . 25 hence, relative permittivity is 2 . 25 ..