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 $K$, 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) To produce a sustained interference , coherent sources are compulsory , reasons are below ,

(1) If the sources are not coherent , they cannot emit waves continuously .

(2) Independent sources , emit the waves , which don't have same phase or a constant phase difference .

(b) In interference pattern , the intensity $I$ at a point is given by ,

$I=I_0{\cos }^2\left(\pi /\lambda \right)x$

where $x=$ path difference ,

$\lambda =$ wavelength ,

$I_0=$ intensity of central bright fringe ,

when $x=\lambda$ , $I=K$ ,

$K=I_0{\cos }^2\left(\pi /\lambda \right)\lambda =I_0{\cos }^2\pi =I_0$ ,

for $x=\lambda$ , $I=I^{\prime }$ ,

$I^{\prime }=K{\cos }^2\left(\pi /\lambda \right)\lambda /3=K{\cos }^2\pi /3=K\times (1/2{)}^2$ ,

or $I^{\prime }=K/4$ ,