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The angle of a prism is ‘A’. One of its refracting surfaces is silvered. Light rays falling at an angle of incidence 2A on the first surface returns back through the same path after suffering reflection at the silvered surface. The refractive index μ, of the prism is:

1. 2 sin A
2. 2 cos A
3. 1/2 cos A
4. tan A

Correct answer: 2 sin A

Solution

For the light to retrace its path, the angle of incidence at the first surface must equal the critical angle for total internal reflection at the silvered surface. Using Snell's law and geometry, the refractive index μ is found to be 2 sin A.

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