Question 80: Ray Optics

Question

The refractive index of a prism with apex angle $$A$$ is $$\cot A / 2$$. The angle of minimum deviation is :

Accepted Answer

$$\begin{aligned}
& \mu=\frac{\sin \left(\frac{A+\delta m}{2}ight)}{\sin \frac{A}{2}} \
& \frac{\cos \frac{A}{2}}{\sin \frac{A}{2}}=\frac{\sin \left(\frac{A+\delta m}{2}ight)}{\sin \frac{A}{2}} \
& \sin \left(\frac{\pi}{2}-\frac{A}{2}ight)=\sin \left(\frac{A+\delta_m}{2}ight) \
& \frac{\pi}{2}-\frac{A}{2}=\frac{A}{2}+\frac{\delta m}{2} \
& \delta_m=\pi-2 A
\end{aligned}$$

Answer

$$\delta_m=180^{\circ}-3 \mathrm{~A}$$

Answer

$$\delta_m=180^{\circ}-4 A$$

Answer

$$\delta_m=180^{\circ}-2 A$$

Answer

$$\delta_m=180^{\circ}-A$$

Ray Optics

The refractive index of a prism with apex angle $A is \cot A / 2$. The angle of minimum deviation is :

Choose the correct answer: