Question

A ray of light enters from a rarer to a denser medium. The angle of incidence is $i$. Then the reflected and refracted rays are mutually perpendicular to each other. The critical angle for the pair of media is

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

Answer 1

Answer: (C)

${\sin }^{-1}\left(\cot i\right)$

So $i+r=\frac{\pi }{2}$

$sini=\mu sinr$

$\mu =tani$

$\mu sinc=1$

$c=si{n}^{-1}coti$