Question

The angle of incidence for an equilateral prism is ${60}^{\circ }$. What should be the refractive index of prism so that the ray is parallel to the base inside the prism?

• A. $\sqrt{2}$
• B. $\sqrt{3}$
• C. $\frac{4}{3}$
• D. $\frac{9}{8}$

Answer 1

The correct option is B $\sqrt{3}$

For an equilateral prism the ray inside the prism will be parallel to the base at minimum deviation.
At minimum deviation $r_1=r_2=\frac{A}{2}={30}^{\circ }$
$\therefore \mu =\frac{sin{i}_1}{sin{r}_1}=\frac{sin{60}^{\circ }}{sin{30}^{\circ }}=\frac{\left(\frac{\sqrt{3}}{2}\right)}{\left(\frac{1}{2}\right)}$
or $\mu =\sqrt{3}$