Question

A ray of light form a denser medium strikes a rarer medium at angle of incidence i. The reflected and refracted rays make an angle of 90 degrees with each other. The angle of reflection and refraction are r and r' resp. the critical angle is?

Answer 1

given, incidence angle = i

retracted angle = r'

reflected angle = r

and angle between reflected and refracted rays = 90°

e.g., r + r' = 90° ........(1)

from Snell's law,

$\mu sini=1\times sinr'$

or, $\mu sini = sin(90^{\circ}-r)$

[ from equation (1), ]

or, $\mu sini = cosr$

from law of reflection,

incidence angle,i = reflection angle, r

so, $\mu sinr=cosr$

or, $\mu=\frac{1}{tanr}$......(2)

we know, $sini_c=\frac{1}{\mu}$

from equation (2),

$sini_c=tanr$

or, $i_c=sin^{-1}(tanr)$

hence, critical angle is $sin^{-1}(tanr)$

Answer 2

here is the answer for you dear