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

Answer

B

Explanation

d = 2 mm , D = 2 m
Fringe width for first wave length 12000 Å
`beta_(1)=(lambda_(1)D)/(d)=(12000xx10^(-10)xx2)/(2xx10^(-3))=1.2xx10^(-3)m=1.2mm`
For second length
`beta_(1)=(lambda_(2)D)/(d)=(10000xx10^(-10)xx2)/(2xx10^(-3))=1 mm`
At 6 mm distance from center bright fringe `5^(th)` fringe of rirst coincides with `6^(th)` of second.