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$\bullet$ Two rectangular pieces of plane glass are laid one upon theother on a table. A thin strip of paper is placed between them atone edge, so that a very thin wedge of air is formed. The platesare illuminated at normal incidence by 546 nm light from amercury-vapor lamp. Interference fringes are formed, with15.0 fringes per centimeter. Find the angle of the wedge.

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$0.02345^{\circ}$

Physics 102 Electricity and Magnetism

Physics 103

Chapter 26

Interference and Diffraction

Electromagnetic Waves

Reflection and Refraction of Light

Rutgers, The State University of New Jersey

Simon Fraser University

Hope College

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.

07:04

Two rectangular pieces of …

35.29. Two rectangular pie…

01:32

Two plane glass plates are…

Two plene glass plates are…

02:49

A narrow beam of light is …

01:56

02:08

$\bullet$$\bullet$ A beam …

03:24

$\bullet$ A beam of light …

01:24

A beam of unpolarized ligh…

In this case, the light is traveling through the glass, and then it hits a layer of air. And since the index of refraction for glasses greater than air, there will not be a 1 80 faces there. But when the light enters the air and then hits the next layer of glass, there will be a 1 80 phase shift. So the point is that there is a net 1 80 phase shift here in this problem, and that means the condition for constructive interference is going to be two times T is equal to M plus 1/2. It's a wavelength and announce sketched the geometry of the problem. So this bottom part is the bottom layer of glass. We have our wedge of there and we have another layer of glass here, and I exaggerated the angle of this tilt here. Let the distance between these two BT, whenever the distance from this spot is X, and they were gonna let the angle here be safe. And the angle is what we're actually trying to solve for here. And so tangible data from the graph or from from this picture is equal to t over X and so tea is equal to X tangent data. And we know based on this that the tea that produces a max is equal to M plus 1/2 time's land O R. Two and then playing this into here in the sewing for the X that produces a max gives one plus 1/2 time's landa over to tangent of data. Now, if we know that this is an ex value that produces a max, what is the X value that produces next? Max? We'll be ex of implicit one, and so it beyond plus three halves Time's land over to tangent data. And so what's the distance between the X values that produced maximums? Maxima? Well, we're going to take the difference between these two. So Excel plus One minus Excel is equal to Delta X and this when you do, how is equal to Landover? Two time stand off data. Now it's set this aside for a second. They tell us that we have 15 fringes per cent here and so we can set up a proportion to figure out how many centimeters for one fringe. And so we have one for engine. We want to figure out What's the delta acts for? One fringe. If you solve this proportional, you get that. The delta axes 0.667 centimeters. So this is the actual distance between the French is based on what they give us, and then we calculated, based on theoretical grounds what that should be. So it could take this and plug it back in here and figure out what Tanja thing. That must be. Be careful. Tto switch the units on this to the units are you using for Lambda here? They have to match for this to make sense. Tanja Theta ends up being 4.9 times 10 to the negative for and so theta is equal to 4.9 times 10 to the negative. For this is radiance. You'll note that this is exactly equal to this because we're operating in a small angle approximation. If you switch this two degrees, you'll get data is equal to 0.23 four degrees. So this helps you really see that it's a small angle approximation because that's a really small angle. That's the final answer

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