A ray of light is incident on a transparent glass slab of refractive index $1.62$ . If the reflected and refracted rays are mutually perpendiculars, what is angle of incidence?

Question

$(a)\;\tan^{-1} 1.31 \\ (b)\;\tan ^{-1} 1.5 \\ (c)\;\tan ^{-1} 1.62 \\ (d)\;\tan ^{-1} 2.5 $

Answer 1

http://clay6.com/mpaimg/jee%20p%2016%20n19.JPG

Let angle of incidence , angle of reflection and angle of refraction be i, r and r' respectively

as per the question ,

$90-r +90 -r'=90$

=> $r'= 90-i$ (because $i=r$ in case of reflection according to Snell's law )

$1 \sin i =y \sin r$

or $\sin i =y \sin r'$

or $\sin i =y \sin (90-i)$

=> $\tan i =y$

or $i=\tan ^{-1} y$

$\qquad= \tan ^{-1} 1.62$

Hence c is the correct answer.