Question

An equilateral prism is made of material of refractive index $\sqrt{3}$. The angle of minimum deviation through the prism is:

• A. $60\degree$
• B. $30\degree$
• C. $45\degree$
• D. $0\degree$

Answer 1

Answer: (B)

$30\degree$

Answer 2

\text{ The relation between the refractive index } n, \text{ the angle of the prism } A, \text{ and the minimum deviation } D_{\text{min}} \text{ is given by the formula:}$$$n = \frac{\sin \left( \frac{A + D_{\text{min}}}{2} \right)}{\sin \left( \frac{A}{2} \right)}$$ \text{Here, the refractive index } n = \sqrt{3}, \text{ and for an equilateral prism, the angle of the prism } A = 60^\circ.$$\text{ Substituting these values:}$$$\sqrt{3} = \frac{\sin \left( \frac{60^\circ + D_{\text{min}}}{2} \right)}{\sin(30^\circ)}$$
$\text{Solving for } D_{\text{min}}, \text{ we find that } D_{\text{min}} = 30^\circ.$