Ray Optics Question 10
Question 10 - 2024 (31 Jan Shift 1)
The refractive index of a prism with apex angle $A$ is $\cot A / 2$. The angle of minimum deviation is :
(1) $\delta _m=180^{\circ}-A$
(2) $\delta _m=180^{\circ}-3 A$
(3) $\delta _m=180^{\circ}-4 A$
(4) $\delta _m=180^{\circ}-2 A$
Show Answer
Answer: (4)
Solution:
$\mu=\frac{\sin \left(\frac{A+\delta m}{2}\right)}{\sin \frac{A}{2}}$
$\frac{\cos \frac{A}{2}}{\sin \frac{A}{2}}=\frac{\sin \left(\frac{A+\delta m}{2}\right)}{\sin \frac{A}{2}}$
$\sin \left(\frac{\pi}{2}-\frac{A}{2}\right)=\sin \left(\frac{A+\delta _m}{2}\right)$
$\frac{\pi}{2}-\frac{A}{2}=\frac{A}{2}+\frac{\delta m}{2}$
$\delta _m=\pi-2 A$
