Question

A ray of light from a denser medium strikes a rarer medium at an angle of incidence $i$. If the reflected and refracted rays are mutually perpendicular to each other then the critical angle is :

• A. sin${}^{-1}$ (tan i)
• B. cos${}^{-1}$ (tan i)
• C. cot ${}^{-1}$ (tan i)
• D. cosec${}^{-1}$ (tan i)

Answer 1

The correct option is A sin${}^{-1}$ (tan i)

$i+r=90$ where i is the angle of incidence, r is the angle of refraction

$r=90-i$

From Snell's Law, $\mu \times sini=1\times sinr$

$\mu \times sini=sin(90-i)$

$\mu =coti$

${\theta }_{cric}=si{n}^{-1}\left(\frac{1}{\mu }\right)=si{n}^{-1}\left(tani\right)$