Question

The refractive index of a prism for a monochromatic wave is $\sqrt{2}$ & its refractive angle is ${60}^o$ . For a minimum deviation, the angles of incidence will be:

• A. ${30}^o$
• B. ${45}^o$
• C. ${60}^o$
• D. ${75}^o$

Answer 1

The correct option is B ${45}^o$

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

$\sqrt{2}=\frac{sin\left(\frac{{60}^0+D_m}{2}\right)}{sin\frac{{60}^0}{2}}$

On solving $D_m={30}^0$

$D_m=2i-A$

${30}^0=2i-{60}^0$

$i={45}^0$