Question

A ray of light from a denser medium strikes a rare medium at angle of incidence i as shown in the figure. The reflected and refracted rays make an angle of 90°with each other. The angles of reflection and refraction are r and r'. The critical angle between them is

(a) sin^-1(tanr)
(b) sin^-1(tani)
(c) sin^-1(tanr')
(d) tan^-1(tani)

(The figure has an incident ray , a reflected ray , a normal and a refracted ray all lying at the point of incidence and an angle of 90 degree btw reflected and refracted ray)

*(Sir/madam please send a detailed answer along with the explanation of the QUESTION)

Answer 1

from laws of relection;
we know that,
I=r
the angle between reflected and refracted ray is 90 degrees.
so,
r+90+r'=180
r+r'=90
i+r'=90
i=90-r'
sin i=sin (90-r')
sin i=cos r'
From laws of refraction;
μ=sin i/sin r
=cos r'/sin i
1/μ=tan r'
sin ^-1 (1/μ)=sin ^-1 (tan r')
Which is the critical angle