Ray optics

Question

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

Easy

Solution

On reflection from the silvered surface, the incident ray will retrace its path, if it falls normally on the surface.

By geometry, r = A

Applying Snell's law at surface PQ,

$1\mathrm{sin}i=\mu \mathrm{sin}r$

$\mu =\frac{\mathrm{sin}i}{\mathrm{sin}r}=\frac{\mathrm{sin}2A}{\mathrm{sin}A}=\frac{2\mathrm{sin}A\mathrm{cos}A}{\mathrm{sin}A}=2\mathrm{cos}A$

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