Two coherent waves of intensities I₁ and I₂ interfere. Derive the conditions of constructive and destructive interference for the two waves. Also find the intensity of resultant wave at position of constructive and destructive interference.

The intensity of resultant wave at any point, where the two coherent waves of intensities I₁ and I₂ interfere is given by, 
                 ...(1) 
At the point of constructive interference, the intensity of the resultant wave is maximum.
From equation (1), the value of I is maximum if 
                 
                     where n = 0, 1, 2, 3...
The intensity at this point is, 
               
                                   ...(2) 
At the point of destructive interference, the intensity of the resultant wave is minimum.
From equation (1), the value of I is minimum if 
                    
                     where n = 0, 1, 2, 3...
The intensity at this point is, 
                  
                                      ...(3)