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$\bullet$ Three ideal polarizing filters are stacked, with the polarizing axis of the second and third filters at $23.0^{\circ}$ and $62.0^{\circ}$ , respectively, to that of the first. If unpolarized light is incident on the stack, the light has intensity 75.0 $\mathrm{W} / \mathrm{cm}^{2}$ after it passes through the stack. If the incident intensity is kept constant, what is the intensity of the light after it has passed through the stack if the second polarizer is removed?

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32.3 $\mathrm{W} / \mathrm{cm}^{2}$

Physics 102 Electricity and Magnetism

Physics 103

Chapter 23

Electromagnetic Waves and Propagationof Light

Electromagnetic Waves

Reflection and Refraction of Light

University of Michigan - Ann Arbor

Simon Fraser University

University of Winnipeg

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.

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Three ideal polarizing fil…

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Three polarizing filters a…

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Three Polarizing Filters. …

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Unpolarized light of inten…

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Light that passes through …

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Unpolarized light is incid…

to solve this problem. We're going to use the formula that the intensity is equal to the max intensity. So there's the coastline of the angle between the filter squared. And so let's think about all three filters lined up. And so, with all three filters, Linda well, they will have 12 and three than the intensity after the 3rd 1 is going to be equal to 1/2. I know if I not is going in, then after the first filter is gonna be 1/2. I know because it's not polarized here. And then this filter one is literally polarizing and soda linear, and we pull our is a light servings take out half of it. And so now, after the second filter, we're gonna have a co sign of 23 degrees squared, and the 23 degrees comes from the difference between the second filter on the first filter. So the second filters rotated 23 degrees with respect to the first filter, and then now we have the third filter, and so we have coastline of 62 degrees minus 23 degrees, and this is ultimately to get the difference in angle between the third and the second. But since we're not outright, given that we have to do this attraction here and this is against square and so this represents the intensity of the light at the very end, and so many places in you get 0.256 I know solving this equation for I know gives I over a 0.256 and we're given high in the problem. It's 75 watts per square centimeter. And so playing that in gives it, I not of 2 93 wants for soon your squared and so will need that. Now we just have the first and third floor risers, so we're going to remove this one. This means that I, at the end, is going to be equal to 1/2. I know because the 1st 1 is still there, and then we just have co sign of 62 degrees, says the third one's rotated safety to Yuri's with respect to the 1st 1 And that's where. And so this here is equal to 0.110 I not and we know what I'm not is. That's what we found here and so feeling that in gives 32 point to watts per cent of your spirit, and that's the answer

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