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 ﬩ to each other. What is the value of critical angle 

(a) sin^-1 tan i 

(b) sin^-1 cot i 

(c) sin^-1 cos i 

(d) none 

Answer 1

Correct Option :-  (a) sin-1 tan i

Explanation :-

 The situation in accordance with given problem is shown in figure applying Snell’s law at the boundary at c. 

μ_D sin i = μ_r sin r’                                      r’+ r =90 

μ_D sin i = μ_r sin (90-r) 

(incident < reflected & refracted reflected ray & refracted ray are ﬩ to from reflection each other r’+ r =90)

μ_D sin i = μ_r cos r but i=r

μ_D sin i = μ_r cos i 

μ_D /μ_r =cos i/ sin i = cot i 

1/μ = tan i 

but by definition θ_c =sin-1(1/μ) ⇒ θ_c =sin-1(1/μ) 

θ_c =sin-1(tan i)