The angle of a prism is A. One of its refract | vedclass

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(A) For the light ray to retrace its path,it must strike the silvered surface normally (at an angle of $90^{\circ}$).In the triangle formed inside the

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$2 \sin A$

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(A) For the light ray to retrace its path,it must strike the silvered surface normally (at an angle of $90^{\circ}$).In the triangle formed inside the prism,the angle at the silvered surface is $90^{\circ}$,and the angle at the apex is $A$. Thus,the angle of refraction $r$ at the first surface must be $r = 90^{\circ} - A$.According to Snell's Law at the first surface: $\mu = \frac{\sin i}{\sin r}$.Given $i = 2A$ and $r = 90^{\circ} - A$,we have:$\mu = \frac{\sin(2A)}{\sin(90^{\circ} - A)}$$\mu = \frac{2 \sin A \cos A}{\cos A}$$\mu = 2 \sin A$.

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 return back through the same path after suffering reflection at the silvered surface. The refractive index $\mu$ of the prism is:

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