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$\bullet$$\bullet$ A glass plate $(n=1.53)$ that is 0.485$\mu \mathrm{m}$ thick and sur-rounded by air is illuminated by a beam of white light normalto the plate. What wavelengths (in air) within the limits of thevisible spectrum $(\lambda=400 \mathrm{nm}$ to 700 $\mathrm{nm})(\mathrm{a})$ are intensified inthe reflected beam, (b) are cancelled in the reflected light?

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a) 593.64 $nm$ and 423.81 $nm$b) 494.69 nm

Physics 102 Electricity and Magnetism

Physics 103

Chapter 26

Interference and Diffraction

Electromagnetic Waves

Reflection and Refraction of Light

University of Washington

Hope College

McMaster University

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.

02:34

White light reflects at no…

04:41

03:43

A thin coating $(t=340.0 \…

02:31

A beam of light is sent di…

03:44

Light of wavelength $550 \…

02:18

05:31

35.54. White light reflect…

02:25

Light is incident from abo…

04:03

A thin air wedge between t…

Okay, so this is more or less have been a problem. You have first live a glass n equals 1.5 c, sandwiched by air with enables one. Yeah. Yeah. So first thing you always want to do is draw your paths. Blink, blink. So at this first serve surface are light is going from a lower index of refraction to a higher in nexus a fraction. And when that happens, we pick up half of a wavelength phase shift in our interfering light, our second surface blink, blink. We're going from the higher refractive index to a lower one, and that keeps our face shift the same. So if we compare the two of these, they're now half of phase or half a wave like out of phase slot means air. Constructive interference is gonna happen at our half into jurors. With the wavelength to t t is the thickness this guy t is equal in plus 1/2 lambda. Now, this is the wavelength inside the film itself, which has a non unity index of refraction. So we want to write that in terms of the wavelength outside, we're just dividing it by n Similarly, our destructive interference. D'you not PG Destructive interference happens at two. T equals them Landa in our film and convert it to air Lambda by dividing by m All right, so now we're just gonna go through and check out our different values of M and see what we get. So for em equals zero, you're looking for the wavelengths. So it's self Orlando mop. So it landed, Not equals to t and over m plus half. So if I plug in m equals zero, I get to t the sickness of my glass thing News for 0.485 my girl, So 10 to the negative six meters and off. My film is 1.53 and zero plus ax. So that gives me a wavelengths of 29 68 Nana meters, which is super not in the visible spectrum. Hey, so likewise appear if I saw for land or not, is to t n over m so M equals zero That just doesn't work out. We don't have an M equals zero for our first destructive. They start at one sluts. D'oh equals one. So for my constructive interference which was my land and not Cols two tea and over one plus 1/2 this time. Now you get 989 nan meters. And for my destructive interference, my lambda equals to tea. And over one miss me 14 84 centimeters, neither of which are in the visible spectrum. Something constructive over here so that we don't get lost. Destructive. All right, mister, I am equals two, my land. And that is to Tien over two plus 1/2 that gives me 500 and 94 Nana meters, which is in my spectrum. So that's one of my answers in the visible spectrum. And Nichols to over here we have the not equals to tea and 02 Miss me. 742 Nana meters almost, but not quite. I'm so for n equals three duty and over 3.5 You 424 Nana meters, which is just inside in the visible spectrum. No, over here for, um equals three. Get 495 millimeters

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