Question 258: Ray Optics

Question

The refractive index of an equilateral prism is $$\sqrt 2 $$. The angle of emergence under minimum deviation position of prism, in degree, is ___________.

Accepted Answer

Refractive index
$$
\begin{aligned}
& \mu=\frac{\sin \left(\frac{A+\delta \sin }{2}ight)}{\sin \left(\frac{A}{2}ight)} \Rightarrow \sqrt{2}=\sin \frac{\left(\frac{60+\delta \min }{2}ight)}{\sin 30^{\circ}} \\
& \Rightarrow \frac{1}{2}=\sin \left(\frac{60+\delta \min }{2}ight) \Rightarrow 45^{\circ}=\frac{60+\delta \min }{2} \\
& \Rightarrow \delta \min =30^{\circ} \\
& \delta=\mathrm{i}+\mathrm{e}-\mathrm{A} \\
& 	ext { Here, } e=i \\
& 	ext { So, } \delta \mathrm{min}=2 \mathrm{e}-\mathrm{A} \Rightarrow 2 \mathrm{e}=\delta \min +\mathrm{A} \\
& e=\frac{\delta \min +A}{2}=\frac{30^{\circ}+60^{\circ}}{2}=45^{\circ}
\end{aligned}
$$

Ray Optics

The refractive index of an equilateral prism is $\sqrt 2 $. The angle of emergence under minimum deviation position of prism, in degree, is ___________.

Integer / Numeric Answer Type