Question

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

Answer 1

(a) Coherent sources have almost the same wavelength. Coherent sources are necessary to ensure that the positions of maxima and minima do not change with time. Thereby, producing a sustained interference pattern.

(b) Let $I_1=I_2=I$

Let $\varphi$ be the difference between two light waves.

Therefore the resultant intensity

$I_R=I+I=2I+2I=4I$

But $4I=K$

When path difference is $\frac{\lambda }{3}$ phase difference is $\frac{2\pi }{3}$ radius

$I\text{'}R=I+I+2\sqrt{I_1}$

$I\text{'}R=2I+2I(-\frac{1}{2})=2I-I=I$

$\therefore I=\frac{k}{4}$