In Young's double-slit experiment, the slits are `2mm` apart and are illuminated by photons of two wavelengths `lambda_1=12000Å` and `lambda_2=10000Å`. At what minimum distance from the common central bright fringe on the screen `2m` from the slit will a bright fringe from one interference pattern coincide with a bright fringe from the other?

Options

A. `4mm`
B. `3m`
C. `8mm`
D. `6mm`

Answer

D

Explanation

Let `n_(1)` bright fringe of `lambda_(1)` coincides with `n_(2)` bright fringe of `lambda_(2)`. Then
`(n_(1)lambda_(1)D)/(d)=(n_(2)lambda_(2)D)/(d) "or" (n_(1))/(n_(2))=(lambda_(2))/(lambda_(1))=(10000)/(12000)=(5)/(6)`
Let `x` be given distance. `:.x=(n_(1)lambda_(1)D)/(d)`
Here, `n_(1)=5,D=2m,d=2mm=2xx10^(-3)m`
`lambda_(1)=12000Å=12000xx10^(-10)m=12xx10^(-7)m`
`x=(5xx12xx10^(-7)mxx2m)/(2xx10^(-3)m)=6xx10^(-3)m=6mm`