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Question:

The refractive index of the material of a prism is √2 and the angle of the prism is 30°. One of the two refracting surfaces of the prism is made a mirror inwards, by silver coating. A beam of monochromatic light entering the prism from the other face will retrace its path (after reflection from the silvered surface) if its angle of incidence on the prism is?

Zero

60o

30o

45o

Solution:

Using A = r1 + r2
30° = r1 + 0°
or r1 = 30°
Using Snell's Law, 1 × sin i = μ × sin r1
1 × sin i = √2 × sin 30° = √2 × (1/2)
sin i = 1/√2
i = 45°
option 4 is correct