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

Clearly at Q, path difference `=d sin theta`
`rArr b sin theta ~~ b tan theta=(b.y)/d=(b^(2))/(2d)`
Now whenever `(b^(2))/(2d)` will be odd multiple of `(lambda)/2`, these `lambda`' is
will be having minima at point Q
`rArr (b^(2))/(2d)=(lambda)/2, (3lambda)/2,(5lambda)/2,...... rArr lambda=(b^(2))/d, (b^(2))/(3d), (b^(2))/(5d)......`