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. `1 : 2`
B. `2 : 1`
C. `4 : 1`
D. `1 : 1`

Answer

B

Explanation

Resultant intensity
`l=l_(1)+l_(2)+2sqrt(l_(1)l_(2))cosphi`
At central position with coherent source (and `l_(1)=l_(2)=l_(0)`)
`l_(coh)=4l_(0)" "...(i)`
In case of incoherent at a given point, `phi` varies randomly with time so `(cos phi)_(av)=0`
`:." "l_("Incoh")=l_(1)+l_(2)=2l_(0)" "...(ii)`
Hence, `" "(l_("coh"))/(l_("Incoh"))=(2)/(1)`