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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

1. 60°
2. 45°
3. Zero
4. 30°

Correct answer: 45°

Solution

For the light to retrace its path, the angle of incidence on the prism must equal the critical angle for total internal reflection. Using Snell's law and the given refractive index (√2), the critical angle is 45°. Thus, the angle of incidence must also be 45°.

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