Question

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

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

Answer 1

Answer: (D)

$\sqrt{3}$

Given,

The angle of incidence $i={60}^{\circ }$

From the diagram, it can be seen that the angle of refraction is $r={30}^{\circ }$

Now according to Snell’s law

${\eta }_1\sin i={\eta }_2\sin r$

Where ${\eta }_1=1$ ( refractive index of air )

Hence,

${\eta }_2=\frac{\sin i}{\sin r}$

${\eta }_2=\frac{\sin {60}^{\circ }}{\sin {30}^{\circ }}$

${\eta }_2=\frac{\sqrt{3}/2}{1/2}$

Therefore,

${\eta }_2=\sqrt{3}$

The refractive index of glass is $\sqrt{3}$ .