A parallel beam of monochromatic light is used in a Young's double slit experiment. The slits are separated by a distance d and the screen is placed parallel to the plane of the slits. Show that if the incident beam makes an angle `theta=sin^-1(lamda/(2d))` with the normal to the plane of the slits, there will be a dark fringe at the centre P_o of the pattern.

Answer

A

Explanation

The wave fronts reaching O from `S_1 and S_2` will have a path difference of `S_2x`
`sintheta=(S_2X)/(S_1S_2)`
so, path difference `=S_2X`
`=S_1S_2sintheta`
`=dsintheta=dxxlamda/(2d)=lamda/2`
As the path difference is an odd multiple of `lamda/2` there wil be dark fringe at point P.