Question

A prism is made up of material of refractive index $\sqrt{3}$. The angle of prism is $A$. If the angle of minimum deviation is equal to the angle of the prism, then the value of $A$ is

• A. $30^{\circ}$
• B. $45^{\circ}$
• C. $60^{\circ}$
• D. $75^{\circ}$

Answer 1

Answer: (C)

Given $M =\sqrt{3}$ and $\delta_m = A$
Now, $\mu = \frac{\sin\left(\frac{A + \delta_m}{2}\right)}{\sin\left(\frac{A}{2}\right)}$
$=\frac{\sin \left(\frac{A+A}{2}\right)}{\sin \left(\frac{A}{2}\right)}=\frac{\sin A}{\sin \frac{A}{2}}$
$=\frac{2 \sin \left(\frac{A}{2}\right) \cos \left(\frac{A}{2}\right)}{\sin \left(\frac{A}{2}\right)}$
$=2 \cos \left(\frac{A}{2}\right)$
Now. $2 \cos \left(\frac{4}{2}\right)=\mu=\sqrt{3}$
or $\cos \left(\frac{A}{2}\right) \Rightarrow \frac{\sqrt{3}}{2}$
$=\frac{A}{2}=30^{\circ}$
or $A=60^{\circ}$