Ray Optics Question 2
Question 2 - 2024 (27 Jan Shift 1)
If the refractive index of the material of a prism is $\cot \left(\frac{A}{2}\right)$, where $A$ is the angle of prism then the angle of minimum deviation will be
(1) $\pi-2 \mathrm{~A}$
(2) $\frac{\pi}{2}-2 \mathrm{~A}$
(3) $\pi-\mathrm{A}$
(4) $\frac{\pi}{2}-\mathrm{A}$
Show Answer
Answer: (1)
Solution:
$\cot \frac{A}{2}=\frac{\sin \left(\frac{A+\delta_{\min }}{2}\right)}{\sin \frac{A}{2}}$
$\Rightarrow \cos \frac{A}{2}=\sin \left(\frac{A+\delta_{\min }}{2}\right)$
$\frac{A+\delta_{\min }}{2}=\frac{\pi}{2}-\frac{A}{2}$
$\delta_{\text {min }}=\pi-2 \mathrm{~A}$
