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

Given `lambda_(1)=12000 Å` and `lambda_(2)=10000 Å D=2cm` ltbgt and `d=2mm=2xx10^(-3)cm`
We have `lambda_(1)/lambda_(2)=12000/10000=6/5=n_(2)/n_(1)`
`x=(n_(1)lambda_(1)D)/d=(5xx12000xx10^(-10)xx2)/(2xx10^(-3))`
`=5xx1.2xx10^(4)xx10^(-10)xx10^(3)=6mm`