COMEDK Exam 2018 Solved Paper

The angle of incidence =i
Let r be the angle of refraction.
According to given situation, reflected rays and refracted rays are perpendicular to each other.
i.e. ‌‌i+r=90∘ . . . (i)
∴ According to Snell's law,
µ‌=‌

sin‌i

sin‌r

‌=‌

sin‌i

sin‌(90−i)

‌‌[∵‌ From Eq. (i) ‌]
‌=‌

sin‌i

cos‌i

µ‌=tan‌i . . . (ii)
If iC be the critical angle for the pair of media, then
µ=‌

1

sin‌iC

. . . (iii)
From Eqs. (ii) and (iii), we get
‌tan‌i=‌

1

sin‌iC

⇒‌‌sin‌iC‌=cot‌i
⇒‌‌iC‌=sin‌−1(cot‌i)