Question

A Ray of light from denser medium strikes a rare medium at an angle of incidence the reflected and refracted Ray make an angle of 90° with each other the angle of reflection and angle of refraction are r and R find the critical angle

Answer 1

μ = sin i/ sin R

∠r + ∠R + 90° = 180° ( angle on a straight line)

so, ∠r + ∠R = 90°

∴ ∠R = 90° - ∠r           - (1)

Also,   ∠i =  ∠r ( by laws of reflection)

∴ μ = sin r/ sin R

putting (1) in the above equation we get,

μ = sin r/ sin (90-r)

⇒ μ = sin r/ cos r = tan r

now, sin ( critical angle) = μ

and μ = tan r

combining these two,

tan r = sin (critical angle)

∴ critical angle = sin ∧ -1 (tan r)