The refractive index of the material of a prism is $\sqrt{2}$ and its refracting angle is $30^{\circ}$. One…
The refractive index of the material of a prism is $\sqrt{2}$ and its refracting angle is $30^{\circ}$. One of the refracting surface of the prism is made a mirror inward. A beam of monochromatic light entering the prism from the other face will retrace its path after reflection from the mirrored surface if its angle of incidence on the prism is:
$45^{\circ}$
$60^{\circ}$
0
$30^{\circ}$
Solution
Here $\angle r=30^{\circ}$
(Using law of triangle)
$\begin{aligned}
& \Rightarrow \quad \mu=\frac{\sin i}{\sin r} \\
& \Rightarrow \sqrt{2} \cdot \sin 30^{\circ}=\sin i \\
& \Rightarrow \quad \sin i=\frac{1}{\sqrt{2}} \\
& \Rightarrow \quad i=45^{\circ}
\end{aligned}$
(Using law of triangle)
$\begin{aligned}
& \Rightarrow \quad \mu=\frac{\sin i}{\sin r} \\
& \Rightarrow \sqrt{2} \cdot \sin 30^{\circ}=\sin i \\
& \Rightarrow \quad \sin i=\frac{1}{\sqrt{2}} \\
& \Rightarrow \quad i=45^{\circ}
\end{aligned}$