GITAM, Department of Engineering Physics

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Interference 

 

Light is a Wave-Like Disturbance                                               

 

Superposition Principle

The phenomenon of light has proved the validity of the wave theory of light. When two or more wave trains act simultaneously on any particle in a medium, the displacement of the particle at any instant is due to the superposition of all the wave trains.

The displacement of any point due to the superposition of wave systems is equal to the sum of the displacements of the individual waves at that point; "the principle of superposition is the basis of the wave theory of light"

Also after the superposition, the region of crossover, the wave trains emerge as if they have not interfered at all. Each wave train retains its individual characteristics. Each wave train behaves as if others are absent. This was explained by Huygen in 1678 and is known as the Superposition Principle.

 The phenomenon of interference of light is due to the superposition of two wave trains within the region of cross over. There is no loss of energy due to interference. 

 

Constructive Interference                                                        

Waves from two sources start out in phase. Constructive interference occurs if:       d2 - d1 =  n l      n = 0, 1, 2, 3, ..... ---------------------------------- Difference must be an integer number of wavelengths

Destructive Interference                                                                                         

Waves from two sources start out in phase. Destructive interference occurs if: d2 - d1 =  (2n + 1) (l/2)       n = 0, 1, 2, 3, .... ---------------------------------- Difference must be an odd half-integer number of wavelengths.

Interference of Waves from Two Sources                                             

In some places the water wavefronts are in phase (bright spots). In other places the fronts overlap with peak and valley and interfere destructively (darker spots).

 

Young's Double Slit interference    

 

Constructive Interference                                                                                        

For a bright band at P:     l = d sin q     or   2l = d sin q     or   3l = d sin q         etc For a given  l, bright bands occur at sin q =      0                        =     l/d                      =  2 l/d                       =  3 l/d  d sin q = m l,       m = 0, 1, 2, ....

 

 

 

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