Question

The refracting angle of prism is A and refractive index of material of prism is $\cot \frac{A}{2}$ The angle of minimum deviation is

• A. $180^{\circ }-3A$
• B. $180^{\circ }+2A$
• C. $90^{\circ }-A$
• D. $180^{\circ }-2A$

Answer 1

Answer: (D)

$n=\frac{\sin \left(\frac{A+d_m}{2}\right)}{\sin \left(\frac{A}{2}\right)}$
$\Rightarrow \cot \left(\frac{A}{2}\right)=\frac{\sin \left(\frac{A+d_m}{2}\right)}{\sin \left(\frac{A}{2}\right)}$
$\Rightarrow \frac{\cos \left(\frac{A}{2}\right)}{\sin \left(\frac{A}{2}\right)}=\frac{\sin \left(\frac{A+d_m}{2}\right)}{\sin \left(\frac{A}{2}\right)}$
$\Rightarrow \sin \left(90-\frac{A}{2}\right)=\sin \left(\frac{A+d_m}{2}\right)$
$\Rightarrow 90-\frac{A}{2}=\frac{A+d_m}{2}$
$\Rightarrow 180-2A=d_m$