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(gtgtb)` 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 wavelength are

Options

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

Answer

A, C

Explanation

Clearly at Q, path difference `=dsintheta`
`impliesbsintheta=btantheta=(b.y)/(d)=(b^(2))/(2d)`
Now whenever `(b^(2))/(2d)` will be odd multible of `(lamda)/(2)` those `lamda`'s will be having minima at point Q.
`Implies(b^(2))/(2d),(lamda)/(2),(3lamda)/(2),(5lamda)/(2)`
`implieslamda=(b^(2))/(d),(b^(2))/(3d),(b^(2))/(5d)` ..