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A narrow ray of light falls normally on the hypotenuse face of a 30-60-90 prism (refractive index mu = 2.1) kept in air. The ray undergoes total internal reflection at both the shorter faces and exits normally through the hypotenuse. The total clockwise angular deviation of the ray is 2*pi/N radians, where N (not equal to 2). Find N.

1. 2
2. 3
3. 4
4. 6

Correct answer: 3

Solution

Critical angle = arcsin(1/2.1) approx 28.4 deg. The ray enters normal to the hypotenuse (no deviation). It hits the 60 deg face at 60 deg (TIR), reflects to the 30 deg face at 30 deg (TIR again), then exits normal to the hypotenuse. Two TIR bounces inside a 30-60-90 prism produce a net 120 deg (= 2*pi/3) clockwise deviation, giving N = 3.

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