A prism has a refracting angle of 30^circ and | vedclass

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(C) For a ray to retrace its path after reflection from a silvered face,it must strike the silvered face normally (at $90^\circ$ to the surface).In a

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$45^\circ$

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(C) For a ray to retrace its path after reflection from a silvered face,it must strike the silvered face normally (at $90^\circ$ to the surface).In a prism,the angle of refraction at the first surface is $r_1$. The angle of incidence at the second surface is $r_2$. For normal incidence at the second surface,$r_2 = 0^\circ$.Using the relation $A = r_1 + r_2$,where $A = 30^\circ$ is the prism angle,we get $r_1 = A - r_2 = 30^\circ - 0^\circ = 30^\circ$.Applying Snell's Law at the first surface: $\mu = \frac{\sin i}{\sin r_1}$.Given $\mu = \sqrt{2}$ and $r_1 = 30^\circ$,we have $\sqrt{2} = \frac{\sin i}{\sin 30^\circ}$.$\sin i = \sqrt{2} 	imes \sin 30^\circ = \sqrt{2} 	imes \frac{1}{2} = \frac{1}{\sqrt{2}}$.Therefore,$i = 45^\circ$.

$A$ prism has a refracting angle of $30^\circ$ and a refractive index of $\sqrt{2}$. One of its faces is silvered. At what angle of incidence $i$ should a ray be incident on the other face so that it retraces its path after reflection from the silvered face?

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