The critical angle for light going from medium X into medium Y is `theta` . The speed of light in medium X is v. The speed of light in medium Y is

Options

A. `(V_(x))/(tan theta)`
B. `v_(x) sin theta`
C. ` v_(x) tan theta`
D. `(V_(x))/( sin theta)`

Answer

D

Explanation

The critical angle is that angle on incidence in the denser medium for which the angle of refraction in rarer medium is `90^(@)`, i.e.
`rArr " " (sin theta)/(sin 90^(@)) = (mu_(y))/(mu_(x))`
`rArr " "sin theta = (mu_(y))/(mu_(x))" "....(i)`
Where `mu` = refractive index of medium .
Also `mu =("speed of light in vacuum ")/("speed of light in medium") = (c)/(v)" "....(ii)`
From Eq.(i) and (ii) , we get
`sin theta =(c)/(v_(y))xx(v_(x))/(c) = (v_(x))/(v_(y)) rArr v_(y) = (v_(x))/(sin theta)`
Thus, the speed o flight in medium y is `(v_(x))/(sin thet)`