Refraction of light

The phenomenon of change in path of the light, when it goes from one medium to another medium is called refraction of light.

There are two laws of reflection:

1. The incident ray, the refracted ray and the normal to the surface at the point of incidence all lie in one plane.

 

2. Snells laws -

For any two given pair of mediums, the ratio of the sine of the angle of incidence to the sine of the angle of refraction is a constant.

µ =  sin i / sin r = constant for any two given pair of medium

Mathematical form of Snells law

Consider Medium 1 and Medium 2. Light travels from Medium 1 to Medium 2 and suffers refraction.Let the velocity of the light in medium 1 and medium 2 be v₁ and v₂ respectively.

Hence, sin i / sin r = v₁ / v₂  

Refractive index of a medium is defined as the ratio of speed of light in vacuum / air to the speed of light in the medium. It is represented as µ

µ₂ / µ₁ = sin i / sin r

µ₁ sin i = µ₂ sin r

Note -

1. Suppose V₂ > V₁ , that is if medium 2 is lighter, then y > x means the refracted ray bends away from the normal.
2. But if, V₂ < V₁, that is if medium 2 is heavier, then y < x means the refracted ray bends in towards the normal.

Proof –

Case : Rarer medium to denser medium:-

 

The waves generated in medium 1 will have velocity as v₁τ.

Waves in denser medium will have lesser velocity as compared to velocity in rarer medium. It is given as v₂τ.

The wave front will not be a circle as the waves in two different mediums are travelling with different velocities.

 

 

To prove Snell s law:-

Consider two triangle’s ABC and AEC :-

In triangle ABC sin i= (BC/AC) and sin r=(AE/AC)

 By dividing (sin i/sin r) = (BC/AC) x (AC/AE)

Therefore (sin i/sin r) = (BC/AE) =(v₁τ) /(v₂τ)

=> (sin i/sin r) =(v₁/v₂)

Refractive index n; =(c/V) 

Where c = velocity of light in vacuum and V=velocity of light in medium.

Therefore (sin i/sin r) = (c/n₁)/(c/n₂)

Where n₁ and n₂ are the refractive index in medium 1 and 2 respectively 

Snell s law (sin i/sin r) = (n₁/ n₂). Hence proved.

 

Case 1: Angle of incidence is greater than angle of refraction, i>r

Light rays bend towards the normal when it travels from rarer medium to denser medium.

=> v₁> v₂

Where v₁ = velocity in denser medium and v₂ =velocity in rarer medium.

Case 2: Angle of incidence is less than angle of refraction, i<r.

Light rays bend away from the normal when it travels from denser medium to rarer medium.

=>v₁< v₂