Question

the absolute refractive indices of glass and water are 4/3 and 3/2 respectively. if the speed if light in glass is 2x10^8, calculate the speed of light in
1. vacuum
2. water

Answer 1

Refractive index of a medium is defined as the ratio of speed of light in vacuum to speed of light in the medium.

given $v_g=2 \times 10^8\ m/s$ 
Let velocity in vacuum = v
refractive index of glass is 3/2. 
(you have given wrong information.)

$\eta_g = \frac{v}{v_g} \\ \\ \frac{3}{2}= \frac{v}{2 \times 10^8} \\ \\v= \frac{ 3 \times 2 \times 10^8}{2}= 3 \times 10^8\ m/s$

So speed of light in vacuum is $3 \times 10^8\ m/s$.

$\eta_w= \frac{v}{v_w}\\ \\ \frac{4}{3}= \frac{3 \times 10^8}{v_w} \\ \\ v_w= \frac{3 \times 3 \times 10^8}{4} =2.25 \times 10^8\ m/s$

So speed of light in water is $2.25 \times 10^8\ m/s$

Answer 2

Answer:

Explanation:

Solution :-

Refractive index of a medium = Speed of light in air/Speed of light in medium

3/2 = Speed of light in air/2 × 10⁸ m/s

Speed of light in air = 3 × 10⁸ m/s

1. In Vacuum -

Speed of the light in vacuum = 2 × 10⁸ m/s/3/2

Speed of the light in vacuum = 3 × 10⁸ m/s

Hence, the speed of light in vacuum is 3 × 10⁸ m/s.

2. In Water -

Speed of the light in water = 3 × 10⁸ m/s/4/3

Speed of the light in water = 2.25 × 10⁸ m/s

Hence, the speed of light in water is 2.25 × 10⁸ m/s.