**Concept:** What is an Electromagnetic Wave?

Hey guys, in this video we're going to start talking about light and electromagnetic waves. So first we want to start by asking and answering the question what is an electromagnetic wave exactly? Alright let's get to it. An electromagnetic wave which is what light is made out of is composed of oscillating electric and magnetic fields.

So that's basically what light is. Light is just a wave formed of oscillating electric and magnetic fields. I have a picture right here of one of the most common representations of an electromagnetic wave which is an electric field oscillating sinusoidially in the X direction, a magnetic field oscillating sinusoidally in the Y direction and the whole thing propagating in the Z direction you can see the velocity right here propagating in the Z direction. Now at what speed does this light travel? Speed is a very important thing to know for a wave if you want to relate things like the wavelength of the wave to the frequency of the wave. The speed of light in a vacuum is given by this equation, one over the square root of the vacuum permittivity and the vacuum permeability and its 3 times 10 to the 8 meters per second. Now this is a fundamental constant of the universe, the speed of light in a vacuum is constant. When light travels in a vacuum it always travels at this speed, 3 times 10 to the 8 meters per second. Now when it enters air, when it enters water, glass, oil, any other kind of medium, light will travel at a different speed and that speed can change depending on the color of the light and the properties of the medium but in a vacuum it is always C. Always C, 3 times 10 to the 8 meters per second. Typically in a medium you'll write speed of light like I did here with a V.

Let's do a quick example. Blue light with a wavelength of 450 nanometers travels through a medium where the permittivity is 4 times the vacuum permittivity and the permiablility is just the vacuum permeability. What is the speed of the blue light in this medium? The speed of the light in any medium is actually the exact same equation except you put whatever the permittivity and permeability are in that medium instead of in the vacuum. So this is going to be one over all I'm going to substitute are these two things given right here. So this is 4 epsilon not mu not. I can pull that 4 out of the square root as a 2 and if you notice what I have right here, this one over the square root of epsilon not mu not, is just the speed of light and I still have a 2 in the denominator. So this is just going to be the speed of light divided by 2 which is 1.5 times 10 to the 8 meters per second. We did not have to know what 4 times the permittivity was right we know the permittivity is 8.5 times 10 to the -12, the permeability is 4 Pi times 10 to the -7, those are just constants but we don't actually have to plug them in. This is a proportionality problem so all we have to do is work the proportions. Now electromagnetic waves satisfy the following three properties, they are always going to be transverse waves. Remember that longitudinal waves propagate along the oscillation direction, transverse waves propagate perpendicular to the oscillation direction. If you remember in the figure above we had a oscillating electric fields in the X direction, oscillating magnetic fields in the Y direction and the propagation was in the Z direction. Obviously the Z direction is perpendicular to both the X direction where the electric field oscillates and the Y direction where the magnetic field oscillates. So yes this is a transverse wave.

The speed of light actually defines the ratio between the amplitude or that maximum electric field and the amplitude or the maximum magnetic field where E, this maximum electric field or the amplitude of those electric field oscillations equals C, the speed of light, times B. So this ratio is always going to be true that C equals E over B if I just divide this B over. That ratio was always going to equal the speed of light regardless of whether it's in a vacuum as I showed here or it's in a medium. So keep that in mind that the maximum electric field divided by the maximum magnetic field always equals the speed of light in the medium that it's in or in a vacuum if it's not in a medium and lastly unique, completely unique to electromagnetic waves or light, electromagnetic waves do not need a medium to propagate. This is entirely unique to electromagnetic waves and this was actually a very very important thing that was proven at the end of the 1800's early 1900's that led to a lot of brand new physics being done. They used to assume that light propagated in a medium called an ether, they proved that that didn't exist so now we know that light can travel in a vacuum it's the only wave that can, sound cannot, mechanical waves cannot, only light. Alright guys, that wraps up our intro into what exactly electromagnetic waves are. Thanks for watching.

**Problem:** If a lightyear is defined as the distance light travels in one year, what do you think a lightminute is? If Mars is 12 lightminutes away, how far away is it in meters? How long would it take to send a radio transmission to Mars?

The sun is 1.5 × 10 ^{8} km from Earth. The index of refraction for water is 1.263. How much longer would it take light from the sun to reach Earth if the space between them were filled with water rather than a vacuum?

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Which of the following is true about an electromagnetic wave propagating in a vacuum?

A. The electric and magnetic fields are PARALLEL and |B|=c|E|

B. The electric and magnetic fields are PERPENDICULAR to each other and |E|=c|B|

C. The electric and magnetic fields are PERPENDICULAR to the propagation direction

D. A & B

E. B & C

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Two bursts of light of the same wavelength are emitted simultaneously in parallel beams. Beam 1 passes through 1.6 m of material with index of refraction 1.8 while beam 2 passes through a material of index of refraction 2.3. What is the length of the second material so that both beams emerge from their respective materials at the same time?

(1) 1.25 m

(2) 2.04 m

(3) 1.60 m

(4) 2.59 m

(5) 1.30 m

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Microwaves of frequency 6.0 GHz travel through a particular material of length 26.0 m at a speed 15% slower than the speed of light in vacuum. Approximately how many complete wavelengths fit inside the material?

(1) 610

(2) 520

(3) 2560

(4) 3250

(5) 3470

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The plot below depicts the electric field component of a linearly polarized, electromagnetic plane wave traveling through vacuum. * E(r,t)* propagates in the negative

a) increase.

b) decrease.

c) stay the same.

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Light travels through a medium with a permittivity of 1.7ε _{0} and a permeability of 2μ_{0}. What is the speed of light in this medium?

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A radio station broadcast at 80 MHz. How long does it take for this radio signal to travel a distance of 2.0 x 10^{7} m through space? (c = 3.0 x 10^{8} m/s)

A) 0.15 x 10^{-2} s

B) 15 ms

C) 6.7 x 10^{-2} s

D) 20 ms

E) 25 ms

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Which one of the following type of electromagnetic wave travels through space and fastest?

A) radio waves

B) infrared

C) ultraviolet

D) microwaves

E) They all travel through space at the same speed.

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The energy that light carries is related to the frequency of the light by the equation

E = hf

where h is a constant equal to 6.626x10 ^{-34} Js. Blue light of wavelength 400 nm passes from air into a medium with an index of refraction of 1.7.

(a) What is the energy of the light in air?

(b) What is the energy of the light in the medium?

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What is the frequency for green light? (λ = 550 nm)

A. 5.45 x 10^{11} Hz

B. 165 Hz

C. 1.65 x 10^{14} Hz

D. 5.45 x 10^{14} Hz

E. 1.65 x 10^{17} Hz

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A 1.83 x 10^{14} Hz electromagnetic wave propagates in carbon tetrachloride with a speed of 2.05 x 10^{8} m/s. The wavelength of the wave in air is closest to:

A) 1390 nm

B) 1490 nm

C) 1240 nm

D) 1640 nm

E) 1120 nm

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Two electromagnetic waves are traveling at the same speed. The wave with the higher wavelength

A) is traveling faster than the other wave.

B) has a higher frequency than the other wave.

C) is traveling slower than the other wave.

D) has a lower frequency than the other wave.

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A 7.55 x 10^{14} Hz electromagnetic wave propagates in carbon tetrachloride with a speed of 2.05 x 10^{8} m/s. The wavelength of the wave in carbon tetrachloride is closest to:

A) 338 nm

B) 272 nm

C) 361 nm

D) 301 nm

E) 397 nm

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When light travels from air to water,

A) its velocity, wavelength and frequency all change.

B) its velocity and wavelength change, but its frequency does not change.

C) its velocity changes, but its frequency and wavelength do not change.

D) its wavelength changes, but its velocity and frequency do not change.

E) It's frequency changes, but its velocity and wavelength do not change.

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Two electromagnetic waves are travelling at the same speed. The wave with the higher wavelength

A) has a lower frequency than the other wave.

B) has a higher frequency than the other wave.

C) is traveling slower than the other wave.

D) is traveling faster than the other wave.

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Light having a frequency in vacuum of 6.0 x 10 ^{14} Hz enters a liquid of refractice index 2.0. In this liquid, its frequency will be

a) 1.5 x 10^{14} Hz

b) 6.0 x 10^{14} Hz

c) 3.0 x 10^{14} Hz

d) 12 x 10^{14} Hz

e) None of the above choices are correct.

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What is the essential difference between microwaves and blue light?

a) There is no essential difference in the nature of microwaves and blue light other than a difference in frequency and wavelength.

b) Blue light is a beam of photons. Microwaves are not photons.

c) One has an electric charge, the other does not.

d) One is a form of radiation, the other is not.

e) One undergoes refraction, the other does not.

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