Question

Refracting angle of a prism is $\theta$ and refractive index of the material of the prism is $\cot \frac{\theta }{2}$. The angle of minimum deviation is

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

Answer 1

The correct option is A ${180}^o-2\theta$

We know that,

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

But given,

$\mu =cos\left(\frac{\theta }{2}\right)$

$cos\left(\frac{\theta }{2}\right)sin\left(\frac{\theta }{2}\right)=sin\left(\frac{\theta +\delta m}{2}\right)$

$\frac{cos\left(\frac{\theta }{2}\right)}{sin\left(\frac{\theta }{2}\right)}sin\left(\frac{\theta }{2}\right)=sin\left(\frac{\theta +\delta m}{2}\right)$

$cos\left(\frac{\theta }{2}\right)=Sin\left(\frac{\theta +\delta m}{2}\right)Sin(90-\frac{\theta }{2})=Sin\left(\frac{\theta +\delta m}{2}\right)180=\theta =\theta +\delta m180-2\theta =\delta m$