Question

A ray of light from a denser medium strikes a rarer medium at an angle of incidence $i$. The reflected and refracted rays make an angle of $\pi /2$ with each other. If the angles of reflection and refraction are $r$ and $r^{\prime }$, then the critical angle will be

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

Answer 1

Answer: (C)

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

$\mu =\frac{\sin r^{\prime }}{\sin i}$
But $r^{\prime }+r={90}^{\circ }$
or $r^{\prime }={90}^{\circ }-r$
$r={90}^{\circ }-r$
$\therefore \mu =\frac{\cos i}{\sin i}$
or $\frac{1}{\sin i_c}=\frac{1}{\tan i}$
or $i_c={\sin }^{-1}\left(\tan i\right)$.