First slide

Young's double slit Experiment

Question

In Young's double slit experiment, the two slits act as coherent sources of equal amplitude A and wavelength $λ .$ In another experiment with the same set up the two slits are 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 to that in the second case is

Moderate

A

1 : 2
B

2 : 1
C

4 : 1
D

1 : 1

Solution

Resultant intensity $I = I_{1} + I_{2} + 2 \sqrt{I_{1} I_{2}} cosϕ$
At central position with coherent source and $I_{1} = I_{2} =$ $I_{0}$
$I_{coh} = 4 I_{0}$ …..(i)
In case of incoherent at a given point, $ϕ$ varies randomly with time so $(cosϕ)_{av} = 0$
$∴ I_{Incoh} = I_{1} + I_{2} = 2 I_{0}$ ….(ii)
Hence $\frac{I_{coh}}{I_{Incoh}} = \frac{2}{1}$

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