In YDSE, find the missing wavelength at `y = d`, where symbols have their usual meaning `(take Dgt gt d)`.

Options

A. `(d^(2))/(D)`
B. `(2d^(2))/(7 D)`
C. `(3d^(2))/(D)`
D. `(d^(2))/(3D)`

Answer

b

Explanation

`Delta x = d sin theta = (d y)/(D)` (approx.)
`Delta x = (d xx d)/(D) = (d^(2))/(D)`
For missing wavelength, destructive interference has to be there at `y = d`.
`(d^(2))/(D) = (lambda)/(2),(3 lambda)/(2) , (5 lambda)/(2)` ,…
`lambda = (2d^(2))/(D) , (2d^(2))/(3D) , (2d^(2))/(5D)`,....