Question

In Young's double-slit experiment, the two slits act as coherent sources of equal amplitude $A$ and of wavelength $\lambda$. In another experiment with the same setup, the two slits are sources of equal amplitude $A$ and wavelenght $\lambda$, but are incoherent. The ratio of intensity of light at the midpoint of the screen in the first case to that in the second case is $x:y$. Then $x+y$ will be equal to

Answer 1

Maximum amplitude & Intensity -

When $\theta =0,2\pi ---2n\pi$ wherein,

$A_{max}=A_1+A_2{I}_{max}={(\sqrt{I_1}+\sqrt{I_2})}^2$

Interference occur only in case of coherent source

$I^{max}={(\sqrt{I_1}+\sqrt{I_2})}^2=4I$

In case of incoherent source there is no interference and hence intensity at point is 2 i.

Ratio = 2:1