Determine the index of refraction and also answer question b. Snell\'s law will

Question

Determine the index of refraction and also answer question b. Snell's law will be useful. Please show all work.

1. We would like to use a prism made of fused silica glass to turn a beam of light by 90° as shown in the figure. n2 glass air n1 Total internal reflection occurs at the back surface of the prism where the incident angle IS 45° a. Determine the index of refraction for the fused silica. b. If the power density of the incident beam is P 10 mW/m2, determine the power density of the beam as it enters back in to the air at the top of the prism.

Explanation / Answer

use snells law as n1 sin A = nb sin B

so

na = 1* sin 90/sin 45

nb = 1.414

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apply malus law as I Io cos^2 theta

so

P = Po cos ^2Theta

P = 10 * cos^2(45)

P = 10/2 = 5 mW./m^2

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