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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 $\mu$, of the prism is:
A
2 sin A
B
2 cos A
C
$\frac{1}{2}\cos A$
D
tan A
Detailed Solution
For the ray to retrace its path it must hit the silvered face normally, so the angle of refraction at the first face is A.
Snell's law: $(1)\sin 2A = \mu\sin A \Rightarrow \mu = 2\cos A$