Question

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 θ = sin ^-1 (λ/-2d) with the normal to the plane of  the slits, there will be a dark fringe at the centre P₀ of the pattern.

Answer 1

It can be seen from the figure that the wavefronts reaching O from S₁ and S₂ will have a path difference of S₂X.

As the path difference is an odd multiple of λ/2, there will be a dark fringe at point P₀.