Question

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

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

Answer 1

The Correct Option is A

$r+r'+990^\circ=180^\circ$
$\therefore \hspace15mm r'=90^\circ-r$
$Futher, \hspace15mm i=r$
Applying Snell's law $\mu_D sin\, i=\mu_R$ sin r'
or $\mu_D sin\, r=\mu_R sin(90^\circ-r)=\mu^R cos r$
$\therefore\, \, \, \, \, \frac{mu_R}{mu_D}=tan\, r, \theta_C=sin^{-1}\Bigg(\frac{\mu_R}{\mu_D}\Bigg)=sin^{-1}(tan\, r)$
$\therefore$ Correct option is (a).