Two ideal slits `S_(1)` and `S_(2)` are at a distance `d` apart, and illuninated by light of wavelength `lambda` passing through an ideal source slit `S` placed on the line through `S_(2)` as shown. The distance between the planes of slits and the source slit is `D.A` screen is held at a distance `D` from the plane of the slits. The minimum value of `d` for which there is darkness at `O` is `(dlt lt D)`

Options

A. `sqrt((3lamdaD)/2)`
B. `sqrt(lamdaD)`
C. `sqrt((lamdaD)/2)`
D. `sqrt(3lamdaD)`

Answer

C

Explanation

`Deltax=(SS_(1)+S_(10))-(SS_(2)+S_(20))`
or `lamda/2=2sqrt(D^(2)+d^(2))-2D" "therefored=sqrt((lamdaD)/2)`