The angle of a prism is A and one of its refr | vedclass

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(C) Given: Angle of prism $= A$,Angle of incidence $i = 2A$.For the light ray to retrace its path after reflection from the silvered surface,it must s

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$2 \cos A$

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(C) Given: Angle of prism $= A$,Angle of incidence $i = 2A$.For the light ray to retrace its path after reflection from the silvered surface,it must strike the silvered surface normally.Let $r$ be the angle of refraction at the first surface. In the triangle formed by the ray inside the prism,the angle at the silvered surface is $90^{\circ}$. Thus,the angle of refraction $r$ is related to the prism angle $A$ by $r + A = 90^{\circ}$ is incorrect here; rather,from the geometry,$r = A$.Using Snell's law at the first surface:$\mu = \frac{\sin i}{\sin r} = \frac{\sin 2A}{\sin A}$Using the trigonometric identity $\sin 2A = 2 \sin A \cos A$:$\mu = \frac{2 \sin A \cos A}{\sin A} = 2 \cos A$

The angle of a prism is $A$ and one of its refracting surfaces is silvered. Light rays falling at an angle of incidence '$2A$' on the first surface return back through the same path after suffering reflection at the silvered surface. The refractive index of the material of the prism is

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