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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 n and wavelength λ, but are incoherent. The ratio of intensities of light at the mid point of the screen in the first case to that in the second case is?

1:2

3:4

2:1

4:3

Solution:

Case 1: coherent sources
x1=nsin(ωt)
x2=nsin(ωt)
xr1=x1+x2=2nsin(ωt)
Ir1=4n²
Case 2: incoherent sources i.e. 90° phase shift
x1=nsin(ωt)
x2=ncos(ωt)
xr2=x1+x2=√2nsin(ωt+π/4)
Ir2=2n²
Ir1:Ir2=2:1