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. $si{n}^{-1}$(tan r)
• B. $si{n}^{-1}$(cot i)
• C. $si{n}^{-1}$(tan r')
• D. $ta{n}^{-1}$(tan i)

Answer 1

Answer: (A)

$r+r^{\prime }+990^{\circ }=180^{\circ }$
$\therefore r^{\prime }=90^{\circ }-r$
$Futher,i=r$
Applying Snell's law ${\mu }_{D}sini={\mu }_R$ sin r'
or ${\mu }_{D}sinr={\mu }_{R}sin(90^{\circ }-r)={\mu }^{R}cosr$
$\therefore \frac{m{u}_R}{m{u}_D}=tanr,{\theta }_C=si{n}^{-1}\left(\frac{{\mu }_R}{{\mu }_D}\right)=si{n}^{-1}(tanr)$
$\therefore$ Correct option is (a).