Question

The refracting angle of a prism is A and refractive index is $\cot (A/2)$. The angle of minimum deviation is

• A. (180° - A)
• B. (180° - 2A)
• C. (90° - A)
• D. (90° - 2A)

Answer 1

Answer: (B)

Here, $u=\cot \frac{A}{2}$
According to prism formula
$\mu =\frac{\sin \left(\frac{A+{\delta }_m}{2}\right)}{\sin \left(\frac{A}{2}\right)}\therefore \cot \frac{A}{2}=\frac{\sin \left(\frac{A+{\delta }_m}{2}\right)}{\sin \left(\frac{A}{2}\right)}$
or $\frac{\cos \left(\frac{A}{2}\right)}{\sin \left(\frac{A}{2}\right)}=\frac{\sin \left(\frac{A+{\delta }_m}{2}\right)}{\sin \left(\frac{A}{2}\right)}$
or $\cos \left(\frac{A}{2}\right)=\sin \left(\frac{A+{\delta }_m}{2}\right)$
or $\sin \left(90^{\circ }-\frac{A}{2}\right)=\sin \left(\frac{A+{\delta }_m}{2}\right)$
or $90^{\circ }-\frac{A}{2}=\frac{A+{\delta }_m}{2}$
or $180^{\circ }=A=A+{\delta }_m$
or ${\delta }_m=180^{\circ }-2A$