(a) Why are coherent sources necessary to produce a sustained interference pattern ?
(b) In Young's double slit experiment using monochromatic light of wavelength `lamda`, the intensity of light at a point on the screen where path difference is `lamda`, is K units. Find out the intensity of light at a point where path difference is `lamda//3`.

Explanation

(a) Coherent source are needed to ensure that the positions of maxima and minima do not change with time.
(b) We know that
`l=l_(1)+l_(2)+2sqrt(I_(1)I_(2)) cos phi`
`rArr l=4l_(0) cos^(2) phi//2 (l_(1)=l_(2)=l_(0))`
For path difference `lambda,` phase difference `phi=2pi`.
Thus, `K=4l_(0) cos^(2) pi=4l_(0)`
When path difference `=(2lambda)/(3)`
Phase difference, `phi=(4pi)/(3)`
Hence, intensity,
`l=4l_(0) cos^(2)(4pi)/(3)=4I_(0)((1)/(2))^(2)=I_(0)=(K)/(4)`