Question

If angle of minimum deviation of a prism is equal to refracting angle of the prism, then refractive index $\mu$ of material of prism satisfies

• A. $1<\mu <\sqrt{2}$
• B. $2<\mu <3$
• C. $\sqrt{2}<\mu <2$
• D. $1<\mu <\sqrt{3}$

Answer 1

The correct option is C $\sqrt{2}<\mu <2$

$\begin{array}{c}i=A\\ S_{min}=2i-A\\ =A\\ \mu =\frac{\sin \left(\frac{S_{min}+A}{}\right)}{\sin \left(\frac{A}{2}\right)}\\ =\frac{sinA}{\sin \frac{A}{2}}=\frac{2\sin \frac{A}{2}\cos \frac{A}{2}}{\sin \frac{A}{2}}\\ \mu =2\cos \frac{A}{2}\\ =2\cos \frac{i}{2}\\ 0<i<\frac{\pi }{2}\\ 0<\left(\frac{i}{2}\right)<\frac{\pi }{2}\\ \frac{1}{\sqrt{2}}<\cos \left(\frac{i}{2}\right)<1\\ \sqrt{2}<2\cos \left(\frac{i}{2}\right)<2\\ \therefore \sqrt{2}<\mu <2\end{array}$

$\therefore$Option $C$ is correct.