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

`n_(1)lambda_(1)= n_(2)lambda_(2)`
`implies (n_(1))/(n_(2))= (10000)/(12000)= (5)/(6)`
`x_("min")= (n_(1)lambda_(1)D)/(d)= (5 xx 12000 xx 10^(-10) xx 2)/(2 xx 10^(-3))= 6mm`