Search any question & find its solution
Question:
Answered & Verified by Expert
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:
Options:
Solution:
1354 Upvotes
Verified Answer
The correct answer is:
$45^{\circ}$
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)
$$
\begin{aligned}
& \Rightarrow \quad \mu=\frac{\sin i}{\sin r} \\
& \Rightarrow \sqrt{2} \cdot \sin 30^{\circ}=\sin i \\
& \Rightarrow \quad \sin i=\frac{1}{\sqrt{2}} \\
& \Rightarrow \quad i=45^{\circ}
\end{aligned}
$$
Looking for more such questions to practice?
Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.