The prism has refracting angle ' $\mathrm{A}$ '. The second refracting surface of the prism is silvered.…
The prism has refracting angle ' $\mathrm{A}$ '. The second refracting surface of the prism is silvered. Light ray falling on first refracting surface with angle of incidence ' $2 \mathrm{~A}$ ', reaches the second surface and returns back through the same path due to reflection at the silvered surface. The refractive index of the material of the prism is
$\frac{1}{2} \sin \mathrm{A}$
$\frac{1}{2} \cos \mathrm{A}$
$2 \sin A$
$2 \cos A$
Solution
Normal incidence at silvered surface
$\therefore \quad \mu=\frac{\sin \mathrm{i}}{\sin \mathrm{r}}=\frac{\sin 2 \mathrm{~A}}{\sin \mathrm{A}}=\frac{2 \sin \mathrm{A} \cos \mathrm{A}}{\sin \mathrm{A}}=2 \cos \mathrm{A}$
$\therefore \quad \mu=\frac{\sin \mathrm{i}}{\sin \mathrm{r}}=\frac{\sin 2 \mathrm{~A}}{\sin \mathrm{A}}=\frac{2 \sin \mathrm{A} \cos \mathrm{A}}{\sin \mathrm{A}}=2 \cos \mathrm{A}$