Question

(a) Two independent monochromatic sources of light cannot produce a sustained interference pattern' Give reason.
(b) In Young's double slit experiment, using monochromatic light of wavelength $\lambda$, the intensity of light at a point on screen where path difference is l, is k units. Find out the intensity of light at a point where path difference is $\lambda$/3.

Answer 1

(a)- The condition for the sustained interference is that both the sources must be coherent(i.e they must have the same wavelength and the same frequency ,and they must have the same phase or constant phase difference)

Two sources are monochromatic if they have the same frequency and wavelength.Since they are independent, i.e. they have different phases with irregular difference,they are not coherent sources.

(b) Wavelength of monochromatic light =$\lambda$

Path difference =$\frac{\lambda }{3}$

So, phase difference, $\phi$=$\frac{2\pi }{\lambda }\times \lambda$

intensity of light= K units

When path difference is $\frac{\lambda }{3,}$ phase difference becomes $\phi$ =$\frac{2\pi }{3}$

intensity of light,$I=4I\frac{{\cos }^2\varphi }{2}$ =4I$\frac{{\cos }^2\pi }{3}$

I=$\frac{k}{4}$ , is the new intensity of light.