State the law of refraction of light that defines the refractive index of a medium with respect to the other. Express it mathematically. How is refractive index of any medium 'A' with respect to a medium 'B' related to the speed of propagation of light in two media A and B? State the name of this constant when one medium is vacuum or air. The refractive indices of glass and water with respect to vacuum are 3f1.and 4/3 respectively. If the speed of light in glass is 210⁸ m/s, find the speed of light in (i)vacuum, (ii) water.

The second law of refraction is also known as Snell’s law of refraction and it states that: the ratio of Sine of the angle of incidence to the sine of refraction is constant for a given pair of media. It establishes a relation between angle of incidence and angle of refraction.

It can be expressed mathematically as follows:

n is constant and is known as refractive index.

The refractive index of any medium 'A' with respect to a medium 'B' related to the speed of propagation of light in two media A and B can be written as follows:

Where, v_B is the speed of light in medium ‘B’ and v_A is the speed of light in medium ‘A’

BⁿA is the refractive index of medium ‘A’ with respect to medium ‘B’

When one medium is vacuum or air and light is going to another medium, then the constant is known as absolute refractive index.

Given: Refractive index of glass,= 3/2

V_w = 4/3

speed of light in glass, u_g =2x10⁸ m/s

Applying the formula:

Putting the above values

Therefore, velocity of light in vacuum is

Now, for calculating the velocity of light in air

Applying the formula:

Therefore, velocity of light in air is 2.25×10⁸ m/s