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One face of the glass prism is silver polished. $A$ light ray falls at an angle of $45^{\circ}$ on the other face. After reflection it is subsequently reflected from the silvered face and then retraces its path. The refracting angle of prism is $30^{\circ}$. The refractive index of the prism is
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$\sqrt{3}$
$\angle r=90^{\circ}-\left[180^{\circ}-\left(90^{\circ}+30^{\circ}\right)\right]$
$\begin{aligned} & =90^{\circ}-\left[180^{\circ}-120^{\circ}\right] \\ & =90^{\circ}-60^{\circ} \\ & =30^{\circ} \\ \angle i & =45^{\circ} \\ \mu \quad & =\frac{\sin i}{\sin r} \mu=\frac{\sin 45^{\circ}}{\sin 30^{\circ}} \\ \mu & =\frac{\frac{1}{\sqrt{2}}}{\frac{1}{2}}=\sqrt{2}\end{aligned}$
$\begin{aligned} & =90^{\circ}-\left[180^{\circ}-120^{\circ}\right] \\ & =90^{\circ}-60^{\circ} \\ & =30^{\circ} \\ \angle i & =45^{\circ} \\ \mu \quad & =\frac{\sin i}{\sin r} \mu=\frac{\sin 45^{\circ}}{\sin 30^{\circ}} \\ \mu & =\frac{\frac{1}{\sqrt{2}}}{\frac{1}{2}}=\sqrt{2}\end{aligned}$
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