Question

A ray of light is incident on a glass at an angle of ${60}^o$. What would be the refractive index of glass, if reflected and refracted rays are perpendicular to each other ?

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

Answer 1

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

The incident ray $1$ will be reflected at an equal angle as reflected ray $2.$

By laws of reflection, $i=r={60}^o$

The refracted ray $3$ is perpendicular to reflected ray $2.$

So by geometry, the angle of refraction $r^{\prime }={30}^o$

Now by Snell's law,

${\mu }_{air}sini={\mu }_{glass}sin{r}^{\prime }$

$\left(1\right)\times sin{60}^o={\mu }_{glass}\times sin{30}^o$

$\frac{\sqrt{3}}{2}={\mu }_{glass}\times \frac{1}{2}$

${\mu }_{glass}=\sqrt{3}$

Option A is the answer.