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.

Options

A. `4I_(0)`
B. `2I_(0)`
C. `I_(0)`
D. zero

Answer

D

Explanation

Clearly at O, no difference of path due to inside motion of rays.
only path difference =`S_(1)Q`
`=d cos(90-theta)`
`=d sin theta`
`=d xx (lambda)/(2d)=(lambda)/2`
so `Deltaphi=(lambda)/2xx(2pi)/(lambda)=pi`
`rArr ` destructive inteference and hence `I_(rms)=0`