Laws Of Refraction and Refractive Index

For a homogeneous and an isotropic medium, the phenomena of refraction is governed by two laws called Laws of Refraction.

1. First Law :  The incident ray,  the normal to the surface of separation, at the point of incidence and the refracted ray, all lie in the same plane perpendicular to the surface of separation.

2. Second Law : The ratio of sine of the angle of incidence to the sine of angle of refraction is a constant quantity for any two media for the same color of light. The constant is called the refractive index of the 2nd medium with respect to first medium and is denoted by µ.

So                                    

                    Sin i /sin r  =  constant  =  ^aµ_b 

                                                                        

where  ^aµ_b   shows that light is traveling from the medium 'a' into the medium 'b'.

i.e. ^aµ_b  represents the refractive index of medium 'b' with respect to medium 'a'.

Refractive index :

The refractive index of a medium with respect to another medium is the ratio of the sine of the angle of incidence to the sine of angle of refraction when light travels from first medium into second medium.   

                                                                      

Absolute Refractive index: When the first medium (a) is vacuum, then

sin i / sin r = µ  , gives the absolute refractive index of medium b.

Refractive Index in terms of Velocity of Light :

When light passes from one medium to another medium, there is change in velocity of light, thus due to this change in velocity of light, there is refraction (bending of light), hence refractive index may also be defined in terms of velocity of light.

The ratio of velocity of light in vacuum to the velocity of light in a medium is known as the refractive index of the medium.

i.e.,                µ = Velocity of light in vacuum / Velocity of light in medium

                      µ = C / v

Velocity , of light in vacuum (C) = 3 x 10⁸ m/s (Approximately)

There are two types of medium depending upon the value of refractive index.

(i) Optically denser medium : The medium in which value of refractive index is more than 1 is called optically denser medium.

i.e.,           
           µ = C/v >> 1 

i.e., value of v (velocity of light in medium is much less than velocity of light in vacuum (C).

(ii) Optically rarer medium : The medium in which value of refractive index is small i.e., less than 1 is called optically rarer medium.

i.e.,         

            µ = C/v << 1