(a) State the laws of refraction of light. Give an expression to relate the absolute refractive index of a medium with speed of light in vacuum.

(b) The refractive indices of water and glass with respect to air are 4/3 and 3/2 respectively. If the speed of light in glass is 2x10⁸ ms^-1, find the speed of light in air and water.

(a) The two laws of refraction of light are as follows:

(i) The incident ray, the refracted ray and the normal at the point of coincidence, lie in the same plane.

(ii) 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:

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

(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 =2 x m/s

Applying the formula:

Putting the above values

Therefore, velocity of light in vacuum is 3×10⁸ m/s

Now, for calculating the velocity of light in air

Applying the formula:

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