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 Po of the pattern.

Explanation

Path difference for point `P_(0)`
`Deltax=d sin theta=d.lambda/(2d)=lambda/2`
At `P_(0)`, dart fringe is formed.