What Angle Does Light Emerge from a Prism?

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Homework Help Overview

The discussion revolves around the behavior of light as it passes through a prism, specifically focusing on the angles of incidence and refraction. The problem involves applying Snell's Law to determine the angle at which light emerges from an equilateral triangular prism with a given index of refraction.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • The original poster attempts to calculate the angles of refraction using Snell's Law but encounters discrepancies in their results. Some participants suggest visualizing the situation with a sketch to clarify the geometry involved. There is a focus on ensuring the angles are correctly referenced to the appropriate faces of the prism.

Discussion Status

Participants are actively engaging with the problem, questioning the assumptions made about the angles and the relationships between the light ray and the prism's faces. Some guidance has been provided regarding the importance of visualizing the scenario, and there is an acknowledgment of a potential misunderstanding regarding the reference angles.

Contextual Notes

The original poster's calculations yield an unexpected result, prompting questions about the setup and the angles involved. There is an emphasis on ensuring clarity in the relationship between the light ray and the prism's geometry, particularly regarding the normals at the points of refraction.

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Homework Statement


A light ray traveling in the horizontal direction is incident onto a prism as shown in the figure. At what angle relative to horizontal does the light ray emerge from the second face of the shown prism if the prism has an index of refraction of 1.5 and is surrounded by air? The cross section of the prism is in the shape of an equilateral triangle.

Homework Equations


Snells Law.

The Attempt at a Solution

Okay, if the light is heading into the left side of the triangle, then the angle it makes with the normal is 30 degrees since the angle the ray to the left side of the triangle would be 60 degrees. That means the refracted ray will make 19.47 degrees with the normal inside the prism. Now, I believe I should do 90 - 19.47 to get the angle that will make a triangle to connect me to the right side of the prism. Then I can do 180-(90-19.47)-60 = 30+19.47 which gets me 49.47 degrees. Now I need the angle normal to the right side so I do 90-49.47 and I get 40.53 degrees. Snells law tells me that the refracted ray on the right side should be arcsin(1.5*sin(40.53)), which is about 77 degrees. This answer is off by 30 degrees for some reason. The answer is 47 degrees but I get 77 degrees.
 
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Draw a rough sketch and see whether the refracted ray is meeting the opposite face of the prism or which face of the prism! Check the angle of 49.47 you have got is between refracted ray and which face of prism. Just do not play with numbers visualize what is happening.
 
Let'sthink said:
Draw a rough sketch and see whether the refracted ray is meeting the opposite face of the prism or which face of the prism! Check the angle of 49.47 you have got is between refracted ray and which face of prism. Just do not play with numbers visualize what is happening.

There's a ray of light going right on the triangle's left face horizontally. It is then refracted downwards and hits the right face. It is then further refracted downwards. The 49.47 degrees should be the angle between the ray of light and the right side of the triangle.
 
OhBoy said:
Snells law tells me that the refracted ray on the right side should be arcsin(1.5*sin(40.53)), which is about 77 degrees. This answer is off by 30 degrees for some reason. The answer is 47 degrees but I get 77 degrees.
That would be with respect to the local normal to the prism. What's the normal's angle with respect to the horizontal? (You were asked for the ray's angle with respect to the horizontal).
 
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gneill said:
That would be with respect to the local normal to the prism. What's the normal's angle with respect to the horizontal? (You were asked for the ray's angle with respect to the horizontal).

Aha! Thank you! The being off by 30 degrees should of really gave it away. Thanks again for your help :)
 

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