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)=12000Å`
and `lambda_(2)=1000Å`
D=2cm
`d=2mm=2xx10^(-3)m`
We have ,
`(lambda_(1))/(lambda_(2))=(n_(2))/(n_(1))=(12000)/(1000)=(6)/(5)`
as `X=(n_(1)lamda_(1)D)/(d)" " (n_(1)=5)`
`=(5xx12000xx10^(-10)xx2)/(2x10^(-3))`
`=5xx1.2xx10^(4)xx10^(-10)xx10^(3)=6mm`