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 ${90}^o$. Then, the relationship between i and $\mu$ is :

• A. $i=ta{n}^{-1}\left(\frac{1}{\mu }\right)$
• B. $cosi=\mu$
• C. $tani=\mu$
• D. $sini=\mu$

Answer 1

Answer: (C)

As situation can be diagrammatically as below (image)
From law of reflection $i=\theta$
Now, $\theta +r+{90}^o={180}^o$
$\Rightarrow i+r+{90}^o={180}^o$
$r={90}^o-i$
Also, from Snell's law :
$\frac{sini}{sinr}=\mu \Rightarrow \frac{sini}{sin({90}^o-i)}=\frac{sini}{cosi}=\mu$
$\Rightarrow tani=\mu$