Minimum thickness of a mica sheet having `mu=(3)/(2)` which should be placed in front of one of the slits in YDSE is required to reduce the intensity at the centre of screen to half of maximum intensity is

Options

A. `lamda//4`
B. `lamda//8`
C. `lamda//2`
D. `lamda//3`

Answer

C

Explanation

Let t be the thickness so corresponding
`Deltax=mut=(3)/(2)t`
also `I_(max)=4I`
so `I'=2I`
We know `I_(R)=I_(1)+I_(2)+2sqrt(I_(1)I_(2))cosphi`
`implies2I=I+I+2sqrt(I^(2))cos((3pit)/(lamda))impliescos((3pit)/(lamda))=0`
`impliescos((3pit)/(lamda))=cos((pi)/(2))`
or `cos((3pi)/(2))` or `(5pi)/(2)`
`implies(3pit)/(lamda)=(pi)/(2)impliest=(lamda)/(6),(3pit)/(lamda)=(3pi)/(2)jimpliest=(lamda)/(2)`
and `(3pit)/(lamda)=(5pi)/(2)impliest=(5lamda)/(6)`