Question

The angle of incidence for a ray of light at a refracting surface of a prism is $45^{\circ}$. The angle of prism is $60^{\circ }$. If the ray suffers minimum deviation through the prism, the angle of minimum deviation and refractive index of the material of the prism respectively, are :

• A. $30^{\circ} ; \sqrt{2}$
• B. $45^{\circ} ; \sqrt{2}$
• C. $30^{\circ} ; \frac{1}{ \sqrt{2}}$
• D. $45^{\circ} ; \frac{1}{ \sqrt{2}}$

Answer 1

Answer: (A)

$i = 45^{\circ} ; A = 60^{\circ} ; \delta_m = 2i - A = 30^{\circ}$
$\mu = \frac{\sin\left(\frac{A + \delta_{m}}{2}\right)}{\sin A/2} = \frac{\sin45^{\circ}}{\sin30^{\circ}} = \frac{1}{\sqrt{2}}. \frac{2}{1} = \sqrt{2} $