State the conditions for constructive & destructive interference of light

(1) Constructive interference (brightness): There is constructive interference at a point and the brightness or intensity is maximum there, if the two waves of light of the same frequency arrive at

the point in phase, i.e., with a phase difference of zero or an integral multiple of 2π radians.

A phase difference of 2π radians corresponds to a path difference λ, where λ is the wavelength of light.

Phase difference = 0, 2π, 4π, 6π, ... rad = n(2π) rad

or path difference = 0, λ, 2λ,3λ .., etc. = nλ

where n =0, 1, 2, 3,4..., etc.

(2) Destructive interference (darkness): There is destructive

interference at a point and the point is the darkest (the intensity of light is minimum, i.e., zero) if the two waves of light of the same frequency &

intensity arrive at the point in opposite phase, i.e., with a phase difference of an odd-integral multiple of π radians. 

A phase difference of 2π radians corresponds to a path difference λ, where λ is the wavelength of light.

 Phase difference = π, 3π, 5π, ... rad = (2m -1)π rad

or path difference = λ/2, 3λ/2, 5λ/2, ..., etc. = (2m-1)λ/2

where m=1, 2, 3, ..., etc.