Interference of light

Interference of light:- 

                 Interference is the phenomenon exhibited by light when two or more light waves superimpose on each other.

                 The resultant light intensity at any point in the region of superposition is different from the intensities due to each wave. It means that the resultant intensity of light changes from point to point in the region of superposition. The modification of light intensity in the region of superposition is called interference of light.

                   In the region of superposition there are some points where the waves superimpose in such a way that the resultant intensity is greater than the sum of the intensities due to individual waves . This is constructive interference. There are some other points where the resultant intensity is less than the sum of the intensities due to individual waves. This is destructive interference.

a) condition for maximum and minimum intensity:

                   If two light waves having same speed  the phase difference between them. Constructive interference is said to take place only when the resultant light intensity is maximum. These points appear to be bright.

When phase difference 𝜹= 0, 2π, 4π, ...., 2nπ

i.e corresponding path difference = 0, λ,2λ,..,nλ.

                  So the condition for constructive interference is that the path difference between the two waves should be an integral multiple of the wavelength λ.

I.e. Path difference = nπ.   Where n = 0,1,2,....

                 Destructive interference is said to take place only when the resultant light intensity is minimum. So these points appear to be dark.

When phase difference,
 𝜹= π, 3π, 5π, ...,(2n+1)π

i.e Corresponding path difference,
=  λ,3λ,5λ,...,(2n+1) λ
    2  2   2                   2

                 If the amplitudes of the waves are not equal, there will not be complete destructive interference. The condition for destructive interference is that the path difference between the two waves should be an odd integral multiple of half the wavelength.

i.e. path difference= (2n+1) λ
where n=0,1,2,3,....

                Thus as the position of the point P on the screen changes, the path difference between the two waves at P changes and the intensity becomes alternatively maximum and minimum. This is called interference pattern.

b) Classification of interference phenomenon: 

Broadly interference phenomenon can be classified into two groups.

                The important condition for steady interference pattern is that the two light source must be coherent. It means the phase difference between them is always constant. Generally such type of light source can be obtained from a single and the same source of light by using different methods. There are two methods for of light by using different methods. There are two methods for producing such coherent sources. These are,

i) Division of wavefront and
ii) Division of amplitude.

                Depending on a particular method, the phenomenon of interference is studied. And so interference phenomenon can be studied under these two categories. i) Division of wavefront method and ii) Division of amplitude method.

i) Division of wavefront method : 

                In this method, the wavefront generated by a particular source ( known as a incident wavefront ) is divided into two separate wavefronts by using some techniques as in case of superimpose on each other gives a stedy interference pattern. Young's experiment , Fresnel's biprism experiment are the examples of interference by division of wavefront.

ii) Division of amplitude method : 

                  In this method, the amplitude of incident wave is divided into two beams by using partial reflection and refraction. ( As in case of Michelson's experiment). Then by using some techniques these two beams superimpose on each other gives a stedy interference pattern. Michelson's interferometer, interference in thin films, Newton's ring  experiment are the examples of interference by division of amplitudes.