First slide

Incoherent sources

Question

In Young's double slit experiment, the two slits act as coherent sources of equal amplitude A and of wavelength $λ$ in another experiment with the same set up, the two slits are sources of equal amplitude A and wavelength $λ$ but are incoherent. The ratio of the intensity of light at the midpoint of the screen in the first case of that in the second case is

Easy

A

1:1
B

1:2
C

2:1
D

$\sqrt{2 : 2}$

Solution

when the tow sources are coherent. then amplitude at mid-point = A+ A = 2A
$I_{1} \propto (2 A)^{2} or I_{1} = k \times 4 A^{2}$
When the two sources are incoherent, then
$I_{2} \propto (A^{2} + A^{2}) or I_{2} = k \times 2 A^{2} \frac{I_{1}}{I_{2}} = \frac{k \times 4 A^{2}}{k \times 2 A^{2}} = 2$

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