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$\bullet$ $\bullet$ Compact dise player. A compact disc (CD) is read fromthe bottom by a semiconductor laser beam with a wavelengthof 790 nm that passes through a plastic substrate of refractiveindex $1.8 .$ When the beam encounters a pit, part of the beamis reflected from the pit and part from the flat region betweenthe pits, so these two beams interfere with each other. (SeeFigure $26.49 . )$ What must the minimum pit depth be so thatthe part of the beam reflected from a pit cancels the part of thebeam reflected from the flat region? (It is this cancellation thatallows the player to recognize the beginning and end of a pit.For a fuller explanation of the physics behind CD technology,see the article "The Compact Disc Digital Audio System," byThomas D. Rossing, in the December 1987 issue of ThePhysics Teacher.)

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110 nm

Physics 102 Electricity and Magnetism

Physics 103

Chapter 26

Interference and Diffraction

Electromagnetic Waves

Reflection and Refraction of Light

Cornell University

Rutgers, The State University of New Jersey

University of Michigan - Ann Arbor

University of Washington

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.

01:29

A compact disk (CD) is re…

02:11

03:35

A compact disc (CD) is rea…

00:18

Compact disc (CD) and digi…

01:17

In a compact disc (CD), di…

01:06

The laser in a CD player m…

06:03

03:58

The laser in a compact dis…

in this case we have that both reflections, the one at the top of the pit and one at the bottom of it occur for waves in the plastic sub stry. And so they're going to have the same face shift associate with, um, there's not gonna be a net. They shift because of that. They do both have a phase shift, but since they both have it, we can essentially ignore the phase shift. We only really care about the net phase shift in these problems. And in this case, we're worried about destructive interference. And so since we have a destructive interference with no net phase shift, the condition is going to be this too. T is equal to film plus 1/2 times the wavelength. This is the wavelength inside of the plastic substrate they almost order. And he is the thickness of the plastic substrate. The two arises from the fact that you have to go through the plastic substrate and they have to go back out. So that's where the two comes from. Now, inside the plastic sub story, our actual lambda here is going to be equal to the Lambda Non outside of the plastic substrate divided by the index of refraction of the plastic substrate. We also want the minimal death pit dip. And so that would be the smallest T value to get the smallest T value in this equation, we're goingto let film zero Now we can let alone be higher values. We just want to get the minimum hit death. We get other deaths, but we want the minimum. So we're gonna have to be zero. So now we have everything we need here. So let's go ahead and solve this for tea. Lt is equal to l'm plus half. I'm slammed over too. I'm going to let lb zero now so that 1/2 combines with this two and I get tea is equal to land over for. And then now I'm going to use this. So this is equal to land a non over foreign and were given that lam not which is the wavelength outside in the airs 7 90 Nana meters. And we're told the index of refraction of the plastic substrate is one pointy. And so this gives 110 Anna Meares. So it's the final answer. That's the thickness that you want here in this place exception substrate

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