Question

The refractive index of a medium 'X' with respect to a medium 'y is 2/3
and the refractive index of medium 'y' with respect to medium 7 is 4/3.
Find the refractive index of medium z with respect to medium 'X'. If the
speed of light in medium 'x' is 3 x 108 ms-, calculate the speed of light
in medium 'y'


CBSE class 10 que 2020​

Answer 1

Answer:

Given :

Refractive index of medium 'x' w.r.t 'y' is 2 / 3

i.e. μ_x / μ_y = 2 / 3 ... ( i )

Also Refractive index of medium 'y' w.r.t. 'z' is 4 / 3

i.e. μ_y / μ_z = 4 / 3 ... ( ii )

We have to find refractive index of  medium 'z' w.r.t. 'x'

i.e. μ_z / μ_x

Now combining ( i ) and ( ii ) we get :

μ_x / μ_z = 8 / 9

= >  μ_z / μ_x = 9 / 8

Therefore refractive index of  medium 'z' w.r.t. 'x' is 9 / 8 .

We know :

Refractive index = Speed of light in vacuum / Speed of light in given medium.

i.e.  μ = c / v

We have given  :

μ = 2 / 3  and c = 3 × 10⁸ m / sec

v = c /  μ

v = 3 × 10⁸ / 2 / 3 m / sec

v = 4.5 × 10⁸  m / sec

Hence speed of light  in medium 'y' is 4.5 × 10⁸  m / sec