An optician directs a beam of light at right angles to the long face (or hypotenuse) of a 45°–45°–90° prism immersed in air, as shown in the figure below. The beam undergoes total internal reflection at each of the two sides making up the legs of the right triangle. For this to occur, what must be the minimum index of refraction for the material making up the prism?   A horizontal ray is normally incident on the long, hypotenuse face of a right-triangular prism. The ray extends unbent to the upper leg of the triangular prism, then reflects to move straight down. The ray is then incident on the lower leg of the triangular prism, and reflects to the left. The ray finally passes unbent through the hypotenuse of the triangular prism and extends to the left.

Principles of Physics: A Calculus-Based Text
5th Edition
ISBN:9781133104261
Author:Raymond A. Serway, John W. Jewett
Publisher:Raymond A. Serway, John W. Jewett
Chapter25: Reflection And Refraction Of Light
Section25.7: Total Internal Refl Ection
Problem 25.6QQ
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An optician directs a beam of light at right angles to the long face (or hypotenuse) of a 45°–45°–90° prism immersed in air, as shown in the figure below. The beam undergoes total internal reflection at each of the two sides making up the legs of the right triangle. For this to occur, what must be the minimum index of refraction for the material making up the prism?
 
A horizontal ray is normally incident on the long, hypotenuse face of a right-triangular prism. The ray extends unbent to the upper leg of the triangular prism, then reflects to move straight down. The ray is then incident on the lower leg of the triangular prism, and reflects to the left. The ray finally passes unbent through the hypotenuse of the triangular prism and extends to the left.
 

 

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