Question

A prism of refractive index $\sqrt{2}$ has a refracting angle of ${60}^o$. At what angle a ray must be incident on it so that it suffers a minimum deviation?

• A. ${30}^o$
• B. ${45}^o$
• C. ${60}^o$
• D. ${90}^o$

Answer 1

Answer: (A)

${30}^o$

For a prism, the angle of minimum deviation,

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

Substituting values,

$\sqrt{2}=\frac{\sin (30+\delta /2)}{\sin 30}$

$\frac{1}{\sqrt{2}}=\sin (30+\frac{\delta }{2})$

$45=30+\frac{\delta }{2}$

$\delta ={30}^o$