Q. What is the angle of incidence for an equilateral prism of refractive index $\sqrt{3}\ $so that the ray is parallel to the base inside the prism?
A) $30{^\circ}$
B) $45{^\circ}$
C) $60{^\circ}$
D) Either $30{^\circ}\ or\ 60{^\circ}$
Explanation
(c) $\sqrt{3} = \frac{\sin\left( \frac{60{^\circ} - \delta_{m}}{2} \right)}{\sin\left( \frac{60{^\circ}}{2} \right)}$
$\frac{\sqrt{3}}{2} = \sin\left( \frac{60{^\circ} + \delta_{m}}{2} \right)$
$\sin{60{^\circ} = \sin\left( \frac{60{^\circ} + \delta_{m}}{2} \right)}$
Or $\frac{60{^\circ} + \delta_{m}}{2} = 60{^\circ}$
Or ${\ \delta}_{m} = 60{^\circ};i = \frac{A + \delta_{m}}{2} = \frac{60{^\circ} + 60{^\circ}}{2} = 60{^\circ}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.