Question

The refractive indices of glass and water with respect to air are 3/2 and 4/3 respectively. If the speed of light in glass is 2 x 10^8 m/s, find the speed of light in water. [2M,2016] a)2.15X10^8 m/s
b) 2.25X10^9 m/s
c)2.25X10^8 m/s
d)1.25X10^8 m/s

Answer 1

Given: The refractive indices of glass and water with respect to air are

$=\frac{3}{2}$ and $\frac{4}{3}$

The speed of light in the glass $= 2*10^8m/s$

To find: The speed of light in water.

Solution:

It is given that the refractive indices of glass and water with respect to air are $=\frac{3}{2}$ and $\frac{4}{3}$

Speed of light in the glass $=2*10^8m/s$

We know the formula for the refractive index in glass is,

The refractive index in glass $=\frac{Speed_of_light_inair}{Speed_of_light_inglass}$

⇒$\frac{3}{2}=\frac{Speed-of-light-in-air}{2*10^8}$

⇒Speed of light in air $=3*10^8$

The formula for the refractive index in water is,

Refractive index $=\frac{Speed-of-light-in-air}{Speed-of-light-in-water}$

⇒ $\frac{4}{3}=\frac{3*10^8}{Speed-of-light-in-water}$

⇒ Speed of light in water $=\frac{3*3*10^8}{4}$

∴Speed of light in water $=2.25*10^8$

Final answer:

The Speed of light in water is c) 2.25 × 10^8.