Question

Light travels through a glass plate of thickness t and refractive index n. If c is the speed of light in vacuum, the time taken by light to travel this thickness of glass is

A. $\dfrac{t}{{nc}}$
B. $tnc$
C. $\dfrac{{nt}}{c}$
D. $\dfrac{{tc}}{n}$

Answer 1

Hint: Velocity of light will be different in different media. If velocity of light is higher in one medium and lesser in another medium then the first one is called a rarer medium and the second one is called denser medium. By finding the dependance of velocity on refractive index of medium we can solve this question

Complete step by step answer:
There are two kinds of waves normally. One will be a transverse wave and the other will be a longitudinal wave. In case of transverse waves the direction of propagation of waves is perpendicular to the direction of vibration of the particles of the medium. Transverse wave has crests and troughs. In case of the longitudinal wave particles of the medium of propagation vibrates in the direction of propagation of the wave. This longitudinal wave has compressions and rarefactions. In case of longitudinal waves particles vibrate in to and fro motion. Transverse waves can propagate without medium too whereas longitudinal waves require medium to propagate. Example for transverse waves is light whereas example for the longitudinal wave is sound.
Velocity is nothing but the rate of change of displacement i.e the ratio of displacement to the time taken. So the time taken will be displacement upon the velocity.
Velocity of light in any medium of refractive index(n) will be
$v = \dfrac{c}{n}$ where ‘c’ is the velocity of light in the free space and ‘n’ is the refractive index of the medium
So the glass slab refractive index is given as ‘n’ and the thickness of the slab is given as ‘t’. Hence the velocity of light in glass slab will be
$v = \dfrac{c}{n}$
Displacement of light in slab will be ‘t’ and the time taken for this be ‘T’ so the relation will be
$\eqalign{
  & t = vT \cr
  & \Rightarrow T = \dfrac{t}{v} \cr
  & \Rightarrow T = \dfrac{t}{{\left( {\dfrac{c}{n}} \right)}} \cr
  & \therefore T = \dfrac{{nt}}{c} \cr} $

Hence option C will be the answer for the question.

Note:
Actually when there is a change in the velocity when light enters the different medium, there will be change in the length travelled too, because let us assume the light entered the rarer medium, then the velocity of light increases and the light will bend away from the normal so that the distance travelled also increases so that the time will be constant. One more thing to be remembered is that the refractive index of any medium can’t be less than one.