Question

A ray of light is travelling through a medium of refractive index $\frac{1}{\sqrt{2}}$ with respect to air. When it is incident on the surface making an angle $45^{\circ}$ with the surface, which of the following will take place?

• A. Angle of refraction will be $45^{\circ}$
• B. Angle of refraction will be $90^{\circ}$
• C. The ray will be internally reflected
• D. None of the above

Answer 1

Answer: (B)

Given, $\mu=\frac{1}{\sqrt{2}}$ w.r.t. air $i=45^{\circ}, r=$ ?
Also, $\mu=\frac{\sin i}{\sin r}$
$\Rightarrow \frac{1}{\sqrt{2}}=\frac{\sin 45^{\circ}}{\sin r}$
$\Rightarrow \frac{1}{\sqrt{2}}=\frac{1 / \sqrt{2}}{\sin r}$
$\Rightarrow \sin r=1$
$\Rightarrow r=90^{\circ}$
Note that the ray is incident from denser medium and is refracted into a rarer medium air.