Question

A ray of light from a denser medium strikes a rarer medium at an angle of incidence i. If the reflected and refracted rays

are mutually perpendicular to each other, what is the value of critical angle?

(A) sin–1 (cot i) (B) sin–1 (tan i). (C) cos–1 (cot i). (D) cos–1 (tan i)​

Answer 1

Explanation:

am using m for refractive index of denser medium and n for refractive index of rarer medium)

According to Snell's law,(product of refractive index and sine of angle remains constant)

m.sin i = n.sinr1; ~ eqn(1)

Now if you draw a figure then you will see that r+r1+90=180

i.e, r+r1=90

but, r=i (property of reflection)

so, r1=90-i ;

putting this in eqn 1

m. sin i = n. sin (90-i) ;

i.e, m.sin i = n. cos(i) ;

n/m = tan i ;

To calculate critical angle ( I take critical angle to be x)

m. sin x = n. sin 90 (Snell's law)

sin x = n/m

i.e, sinx = tan i

therefore, x = sin^(-1) (tan i)

Hope this helps