Solution:-

(i) Refractive index of Glass = Speed of light in Vaccum/ Speed of light in Glass.

3/2 or 1.5 = Speed of light in Vaccum/ 2×10^8.

1.5 × 2×10^8 = Speed of light in Vaccum.

3.0 × 10^8 m/s = Speed of light in Vaccum.


(ii) Refractive index of Water = Speed of light in Water/ Speed of light in Vaccum.

1/3 or 0.33 = Speed of light in Water/ 3.0 × 10^8.

0.33 × 3.0 × 10^8 = Speed of light in Water.

0.33 × 30.0 = Speed of light in Water.

9.9 × 10^8 m/s = Speed of light in Water.

The refractive index of a medium is a measure of how much the speed of light is reduced when it travels through that medium compared to its speed in a vacuum. It is denoted by the symbol 'n'.

Given information:
Refractive index of glass (ng) = 3/2
Speed of light in glass (vg) = 2 x 10^8 m/s

To calculate the speed of light in water and vacuum, we can use the formula:

n = c/v

where 'n' is the refractive index, 'c' is the speed of light in vacuum, and 'v' is the speed of light in the medium.

1. Speed of light in water:
Let's assume the refractive index of water is 'nw' and the speed of light in water is 'vw'. We can set up the following equation:

nw = c/vw

To find the value of 'nw', we need to rearrange the equation:

nw = c/vw
vw = c/nw

Given:
Refractive index of water (nw) = 1/3

Substituting the value of 'nw' in the equation, we get:

vw = c/(1/3)
vw = 3c

Therefore, the speed of light in water (vw) is 3 times the speed of light in vacuum (c).

2. Speed of light in vacuum:
The speed of light in a vacuum is a fundamental constant and is denoted by 'c'. Its value is approximately 3 x 10^8 m/s.

To summarize:
- The speed of light in water (vw) is 3 times the speed of light in vacuum (c).
- The speed of light in a vacuum (c) is approximately 3 x 10^8 m/s.

In conclusion, the speed of light in water is three times the speed of light in a vacuum, and the speed of light in a vacuum is approximately 3 x 10^8 m/s.