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$\bullet$ The lenses of a particular set of binoculars have a coatingwith index of refraction $n=1.38,$ and the glass itself has$n=1.52 .$ If the lenses reflect a wavelength of 525 $\mathrm{nm}$ themost strongly, what is the minimum thickness of the coating?

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The minimum thickness of the coating that would strongly reflect 525 nm wavelength of light is 190.2 nm .

Physics 102 Electricity and Magnetism

Physics 103

Chapter 26

Interference and Diffraction

Electromagnetic Waves

Reflection and Refraction of Light

Cornell University

University of Washington

Simon Fraser University

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.

01:01

A lens with an index of re…

03:32

You're applying a 110…

02:17

An antireflection coating …

01:47

A coating is applied to a …

02:41

A material having an index…

00:53

03:43

A thin coating $(t=340.0 \…

02:23

A transparent film $(n=1.3…

01:33

So let's think about what's happening in this problem. We have light coming in and this is air here and it's hitting this layer and this layer has index of refraction of 1.38 looks like. And after this layer, it's glass which has a much higher index of refraction. It doesn't really matter what it is for calculating thing, this problem, but just know that it is greater then 1.38 And so when this light, which is traveling in air, initially reflects off here, that's going to do that and send small 0.38 is greater than one. There will be 1 80 degree face shift there. Some light will go through and reflect at this interface and travel out like this since one since in glass here the N s a refraction here is greater than 1.38 This will also have a one a degree phase shift. And so between these two, there will be no net phase shift. Now since the lenses reflect 525 Nanami or strongly, we have constructive interference at that wavelength. The condition for constructive interference with no net phase shift is to tea is equal to sometimes Lambda over 1.38 So this land over 1.3 is the land of four. This interface here we just have to divide by this and they're sort of fraction. Lambda is the land out here. But it's not the Lambda in here to get the land. And here we have to divide by the 1.38 So that explains that he is the distance. Here's the thickness and we have to t because this Ray has to go t distant this way and then t distance back out. Really, we want to solve for tea. And so we have to use it to film Lambda over two times 1.38 And for l'm. We're just going to plug in the smallest value, which is one and so put me in There was a little one. We get Lambda over two times 1.38 and now ready to plug in Landa. When we do that, we won 19 animators for tea And so that's the minimum thickness of this layer covering the glass. And that's the final answer

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