Question

A ray of light strikes a glass plate at an angle of ${60}^o$. If the reflected and refracted rays are perpendicular to each other, the refractive index of glass is

• A. $\frac{\sqrt{3}}{2}$
• B. $\frac{3}{2}$
• C. $\frac{1}{2}$
• D. $\sqrt{3}$

Answer 1

Answer: (D)

$\sqrt{3}$

Let the refractive index of the material be $\mu$, and the ange of refraction be $r$.

Since the reflected ray and refracted ray are perpendicular to each other, ${60}^{\circ }+r={90}^{\circ }$

$⟹r={30}^{\circ }$

From snell's law,

$sini=\mu sinr$

$⟹\mu =\frac{sin{60}^{\circ }}{sin{30}^{\circ }}$

$=\sqrt{3}$