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)

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
$\frac{\sin i}{\sin r}=\mu$
$\Rightarrow \frac{\sin i}{\sin \left(90^{\circ }-i\right)}=\frac{\sin i}{\cos i}=\mu$
$\Rightarrow \tan i=\mu$