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$\bullet$ A sinusoidal electromagnetic wave having a magnetic field of amplitude 1.25 $\mu$ and a wavelength of 432 nm is traveling in the $+x$ direction through empty space. (a) What is the frequency of this wave? (b) What is the amplitude of the associated electric field? (c) Write the equations for the electric and magnetic fields as functions of $x$ and $t$ in the form of Equations $(23.3) .$

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$f=6.94 .10^{14} \mathrm{H} z$$E_{\max }=375 \mathrm{V} / \mathrm{m}$$k=1.45 .10^{7} \mathrm{rad} / \mathrm{m}$

Physics 102 Electricity and Magnetism

Physics 103

Chapter 23

Electromagnetic Waves and Propagationof Light

Electromagnetic Waves

Reflection and Refraction of Light

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Lectures

02:30

In optics, ray optics is a geometric optics method that uses ray tracing to model the propagation of light through an optical system. As in all geometric optics methods, the ray optics model assumes that light travels in straight lines and that the index of refraction of the optical material remains constant throughout the system.

10:00

In optics, reflection is the change in direction of a wavefront at an interface between two different media so that the wavefront returns into the medium from which it originated. Common examples include the reflection of light, sound and water waves. The law of reflection says that for specular reflection the angle at which the wave is incident on the surface equals the angle at which it is reflected. Reflection may also be referred to as "mirror image" or "specular reflection". Refraction is the change in direction of a wave due to a change in its speed. The refractive index of a material is a measure of its ability to change the direction of a wave. A material with a higher refractive index will change the direction of a wave to a greater degree than a material with a lower refractive index. When a wave crosses the boundary between two materials with different refractive indices, part of the wave is refracted; that is, it changes direction. The ratio of the speeds of propagation of the two waves determines the angle of refraction, which is the angle between the direction of the incident and the refractive rays.

03:32

A sinusoidal electromagnet…

06:54

03:40

A 550-nm harmonic EM wave …

01:20

An electromagnetic wave of…

07:05

03:19

Suppose that the electric …

05:56

$\bullet$$\bullet \mathrm{…

04:49

07:52

The electric field in a si…

in for a of this problem. We want the frequency and so we can get that from the speed over the wavelengths. And we know the wavelength of these waves. It is 432 times 10 to the minus nine meters and the speed of light. It's just three times 10 to the eight meters per second. And so this ends up being 6.9 for times 10 to the 14th hurts. And that completes part, eh? In part B, we want the maximum electric field. And so we know the maximum electric field is related to the Maxwell magnetic field by the speed of light. So the electric field is larger than the magnetic field by a factor of the speed of light. And so we had this relationship here and they tell us the Maxwell magnetic field and we know the speed of light. And so we can just play. It isn't the Maxwell magnetic field is 1.25 Time's tend to money six teslas and so playing. This inn is 375 and the units on the electric field are volts. The meter, so in part. See, we want to figure out equations for the electric field and magnetic field. And to do that were 1st 1 in the period, which is the inverse of the frequency. And so we can just take this. But I hear an inverted when we get one point for four times 10 to the minus 15 seconds. And now we're going to refer to the formless that they refer to in the book in the General Electric Field is equal to the amplitude of the electric field or the max time sign of to buy times t over the period minus X over the wavelength. And so blinking in our values for the wavelength and the period, both of which are known or we found earlier we it is equal to 3 75 0 And here I'm just plugging in imax, which we found earlier time sign 4.36 times 10 to the 15 radiance per second. And this is Auntie or this is times t teaser variable here and then we're subtracting one point for five times 10 to the seventh meters per second in this part is multiplied by X which, uh okay, I should write that there. She probably used on rotation like that. So we're going to close that up. And that's the equation for the electric field. I forgot my unit's here, but they're in full sperm eater on this 3 75 and so B is very similar is just be Max time. Sign of to buy times multi over Big T, the period minus X over the wavelength. And so plugging in the same exact things. A different value here for Be Max because be Maxine Max or not the same, but promise the same process here. Just going to sit flights down. We get 1.25 times, 10 to the money. Six. Tesla's That's be Max. I'm sign four point 36 stops tend to the 15 radiance per second times time minus 1.45 times 10 to the seventh meters per second, times X, and so that completes the room

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