Critical Angle Prism: Find Theta with n=1.90

[Aeighme]

Homework Statement

A corner reflector is to be made from a triangular prism with index of refraction n = 1.90, as shown in the diagram below. What is the maximum angle, with respect to the normal to the front surface of the prism, (theta), such that total reflection will occur?
http://capa.sci.geneseo.edu/teacher/capalibrary/Graphics/Gtype73/prob02.gif (link to image)

Homework Equations

sin(critical angle)=(n1/n2)

The Attempt at a Solution

Tried using that equation, failed miserably.

 

[tiny-tim]

Hi Aeighme!

sin(critical angle)=(n1/n2)

No … that's the equation for the maximum angle from glass (or whatever) into air.

You need the ordinary sinθ₁/sinθ₂ = n₂/n₁

 

[baba89]

As a scientist, the critical angle prism can be solved by using the equation sin(critical angle) = (n1/n2), where n1 is the index of refraction of the medium the light is coming from and n2 is the index of refraction of the medium the light is entering. In this case, n1=1 (since light is coming from air) and n2=1.90 (since light is entering a prism with an index of refraction of 1.90). Therefore, the critical angle (theta) can be found by taking the inverse sine of (1/1.90), which gives a critical angle of approximately 33.4 degrees. This means that any angle greater than 33.4 degrees will result in total internal reflection within the prism. This information can be used to determine the maximum angle at which total reflection will occur, as requested in the question.