Question

The refracting angle of a prism is A and the refractive index of the material of the prism is $\cot \frac{A}{2}$. 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 $\pi -2A$

It is given $\mu =cotA/2$

We know that:

$\mu =\frac{sin\left(\frac{\delta m+A}{2}\right)}{sinA/2}$

$\Rightarrow cotA/2=\frac{sin\left(\frac{\delta m+A}{2}\right)}{sin\left(A/2\right)}$

$\Rightarrow \frac{cosA/2}{sinA/2}=\frac{sin\left(\frac{\delta m+A}{2}\right)}{sinA/2}$

$\Rightarrow sin(\pi /2-A/2)=sin\left(\frac{\delta m+A}{2}\right)$

$\Rightarrow \pi /2-A/2=\frac{\delta m+A}{2}$

$\Rightarrow \pi -2A=\delta m$