Question

A ray of light from a denser medium strikes a rare medium at an angle of incidence $i$ (see figure). The reflected and refracted rays make and angle of ${90}^{\circ }$ with each other. The angles of reflection and refraction are $r$ and $r^{\prime }$. The critical angle is

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

Answer 1

Answer: (B)

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

As the reflected and refracted rays are at ${90}^0$ then the angle of refraction is $90-i$

According to Snell's law,

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

${\mu }_r=coti$

Critical angle is $si{n}^{-1}\frac{1}{{\mu }_r}=si{n}^{-1}\frac{1}{coti}=si{n}^{-1}\left(tani\right)$