Consider the arrangement shownin figure. By some mechanism,the separation between the slits `S_3 and S_4` can be changed. The intensity in measured at the point P which is at the common perpendicular bisector of `S_1S_2 and S_3S_4. When `z=(Dlamda)/(2d)` the intensity measured at P is I. Find this intensity when z is equal to
a. (Dlamda)/d, b. (3Dlamda)/(2d), c. (2Dlamda)/d`

Answer

A, B, C

Explanation

a. When `z=(lamdaD)/d`
So, `OS_3=OS_4=(lamdaD)/d`
`rarr Dark fringe at `S_3 and S_4`
`rarr At S_3` intensity at `S_3=0`
`rarrl_1=0`
At `S_4 Intensity at S_4=0`
`rarr `l_2=0`
`rarr At P path difference =0
`rarr Phase difference =0`
`rarr l=l_1+l_2+2sqrt(l_1l_2)costheta^@=0+0+0=0`
`rarr intensilty at P=0`