Question

A ray of light is incident at an angle $i$ on a glass slab of refractive index $\mu$. The angle between reflected and refracted light is $90^{\circ}$. Then, the relationship between $i$ and $\mu$ is

• A. $i=\tan ^{-1}\left(\frac{1}{-\mu}\right)$
• B. $\tan \, i = \mu$
• C. $\sin \, i = \mu$
• D. $\cos \, i = \mu$

Answer 1

Answer: (B)

$\tan \, i = \mu$

Answer 2

As situation can be diagrammatically as below

From law of reflection
$i=\theta$
Now, $\theta+I+90^{\circ}=180^{\circ}$
$\Rightarrow i+r+90^{\circ}=180^{\circ}$
$r=90^{\circ}-i$
Also, from Snell's law
$\frac{\sin i}{\sin r}=\mu$
$\Rightarrow \frac{\sin i}{\sin \left(90^{\circ}-i\right)}=\frac{\sin i}{\cos i}=\mu$
$\Rightarrow \tan i=\mu$