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

Question

The angle of a prism is ‘ A ’. One of its refracting surfaces is silvered. Light rays falling at an angle of incidence 2 A 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:

TestHub · Accepted Answer

To retrace its path light rays should fall normally on the reflecting surface. So
$r_{2} = 0$
$\Rightarrow r_{1} = A - r_{2} \Rightarrow r_{1} = A$
Now applying snell rule between incident ray and refracted ray.
$(1) \sin (2 A) = n \sin (A) \Rightarrow 2 \sin A \cos A = n \sin A$
$\Rightarrow n = 2 \cos A$

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