Question

The refracting angle of a prism is A and the refractive index of the material of the prism is $cot\left(\frac{A}{2}\right).$ The angle of minimum deviation of the prism is:

• A. $\pi +2A$
• B. $\pi -2A$
• C. $\frac{\pi }{2}+A$
• D. $\frac{\pi }{2}-A$

Answer 1

The correct option is B $\pi -2A$

$\mu =cot\left(\frac{A}{2}\right)$
$cot\frac{A}{2}=\frac{sin\left(\frac{A+D_m}{2}\right)}{sin\frac{A}{2}}$
$\frac{cos\frac{A}{2}}{sin\frac{A}{2}}=\frac{sin\left(\frac{A+D_m}{2}\right)}{sin\frac{A}{2}}$
$(90-\frac{A}{2})=sin\left(\frac{A+D_m}{2}\right)$
$90-\frac{A}{2}=\frac{A+D_m}{2}$
$90=A+\frac{D_m}{2}$
$D_m=2(90-A)=180-2A$ or $\pi -2A$