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

Answer

C

Explanation

Here, `d = 2 mm = 2 xx 10^(-3)m`,
`lambda_(1) = 12000 Å, lambda_(2) = 1000 Å`
`:. n_(1) lambda_(1) = n_(2) lambda_(2) or (n_(1))/(n_(2)) = (lambda_(2))/(lambda_(1)) = (10000)/(12000) = (5)/(6)`
For minimum distance `x, n_(1) = 5` and `n_(2) = 6`
`:. x_(min) = n_(1)(lambda_(1)D)/(d) = (5 xx (12000 xx 10^(-10)) xx 2)/(2 xx 10^(-3))`
`= 6 xx 10^(-3)m = 6 mm`