White light is used to illuminate the two slits in a Young's double slit experiment. The separation between the slits is b and theh screen is at a distance `d (gt gtb)` from the slits At a point on the screen directly in front of one of the slits, certain wavelengths are missing some of these missing wavelengths are

Options

A. `lambda=b^(2)/(2d)`
B. `lambda=(2b^(2))/d`
C. `lambda=(b^(2))/(3d)`
D. `lambda=(2b^(2))/(3d)`

Answer

C

Explanation

Path difference between the rays reaching in front of slit `S_(1)` is
`S_(1)P-S_(2)P=sqrt((b^(2)-d^(2)))-d`
For destructive interference at P
`S_(1)P-S_(2)P=((2n-1)lambda)/2`
`sqrt((b^(2)+d^(2)))-d=((2n-1)lambda)/2`
`rArrdsqrt((1+b^(2)/d^(2)))-d=((2n-1)lambda)/2`
`rArr d(1+b^(2)/(2d^(2)))-d=((2n-1)lambda)/2`
`rArr beta^(2)/(2delta)=((2v-1)lambda)/2`
`:. lambda=b^(2)/((2n-1)d)`
for `n=1,2....`
`rArrlambda=b^(2)/d, b^(2)/(3d)`