Question

A ray of light from a denser medium strikes a rarer medium at an angle incidence as shown in figure. The reflected and refracted rays make an angle of 90° with each other. The angles of reflection and refraction and r and r¹. The critical angle is

A. sin^-1 (tan r) B. sin^-1 (tan i) 

C. sin^-1 (tan r¹ ) D. tan^-1 (tan i)

Answer 1

According to Snell’s law 

\(\frac{sin\,i}{sin\,r}=μ\)

But I + r = 90° (Reflected and refracted rays are at an angle of 900)

⇒ μ = \(\frac{sin\,90-r}{sin\,r}= \frac{cos\,r}{sin\,r}\)

⇒ μ = cot r.

⇒ μ = \(\frac{1}{tan\,r}\)

⇒ \(\frac1μ \) = tan r

Critical angle = μ = \(\frac{1}{sin\,i_c}\)

⇒ sin i_c = \(\frac1μ \)

⇒ sin i_c =  tan r

⇒ i_c = sin^-1 (Tan r)

Therefore, the critical angle i_c = sin^-1 (tan r) 

Hence the option A is correct.