In Young's double slit experiment, the two slits acts as coherent sources of equal amplitude A and wavelength `lambda`. In another experiment with the same set up the two slits are of equal amplitude A and wavelength `lambda` but are incoherent. The ratio of the intensity of light at the mid-point of the screen in the first case to that in the second case is

Options

A. (a) `1:2`
B. (b) `2:1`
C. (c) `4:1`
D. (d) `1:1`

Answer

B

Explanation

Resultant intensity `I=I_1+I_2+2sqrt(I_1I_2)cosvarphi`
At central position with coherent source and `I_1=I_2=I_0`
`I_(con)=4I_0`
In case of incoherent at a given point, `varphi` varies randomly with time so `(cosphi)_(av)=0`
`:. I_(I n coh)=I_1+I_2=2I_0` ...(ii)
Hence `(I_(coh))/(I_(I n coh))=2/1`.