A ray of light travelling in a denser medium strikes the boundary of a rarer medium. The ray gets partially reflected and refracted. The angle of reflection is r and that of refraction is r' . If the reflected and refracted rays make an angle of 90° with each other then the critical angle for the pair of media is

Question

A ray of light travelling in a denser medium strikes the boundary of a rarer medium. The ray gets partially reflected and refracted. The angle of reflection is r and that of refraction is r' . If the reflected and refracted rays make an angle of 90° with each other then the critical angle for the pair of media is (A) sin-1 (tan r) (B) tan-1 (sin r) (C) sin-1 (tan r') (D) tan-1 (sin r')

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="Solution" src="https://cdn.tardigrade.in/q/nta/p-6nwvx7zkn5fv.png" /> D μR=( sin r/ sin r prime) -----(1) from equation (1) (2) sin C=( sin r/ sin (90-r)) ⇒ sin r= tan r ⇒ C= sin -1 tan r

sin^-1 (tan r)

tan^-1 (sin r)

sin^-1 (tan r')

tan^-1 (sin r')

$D μ_{R} = \frac{s i n r}{s i n r ^{'}}$ -----(1)
from equation (1) & (2)
$sin C = \frac{s i n r}{s i n ( 90 - r )} \Rightarrow sin r = tan r \Rightarrow C = sin^{- 1} tan r$

sin-1 (tan r)

tan-1 (sin r)

sin-1 (tan r')

tan-1 (sin r')

DμR​=sinr′sinr​ -----(1) from equation (1) & (2) sinC=sin(90−r)sinr​⇒sinr=tanr⇒C=sin−1tanr

sin^-1 (tan r)

tan^-1 (sin r)

sin^-1 (tan r')

tan^-1 (sin r')

$D μ_{R} = \frac{s i n r}{s i n r ^{'}}$ -----(1)
from equation (1) & (2)
$sin C = \frac{s i n r}{s i n ( 90 - r )} \Rightarrow sin r = tan r \Rightarrow C = sin^{- 1} tan r$