Question

Two parallel light rays pass through an isosceles prism of refractive index $\sqrt{\frac{3}{2}}$ as shown in the figure. The angle between the two emergent rays is :

• A. ${15}^{\circ }$
• B. ${30}^{\circ }$
• C. ${45}^{\circ }$
• D. ${60}^{\circ }$

Answer 1

The correct option is B ${30}^{\circ }$

from Snell's Law, $\frac{sini}{sin{r}_1}=\sqrt{\frac{2}{3}}$

$i={45}^{\circ }\left(bygeometry\right)$

$\frac{sin{45}^{\circ }}{sin{r}_1}=\sqrt{\frac{2}{3}}$

$sin{r}_1=\sqrt{\frac{3}{2}}$

$r_1={60}^{\circ }$

Let deviation for first ray be $L_1$ and deviation for second ray be $L_2$

$L_1=60-{45}^{\circ }$ $={15}^{\circ }$

Similarly, $L_2={15}^{\circ }$

$\therefore$ Angle between emergent rays $=15+15$ $={30}^{\circ }$