In a Young's double slit experiment, the slits are `2mm` apart and are illuminated with a mixture of two wavelength `lambda_0=750nm` and `lambda=900nm`. The minimum distance from the common central bright fringe on a screen `2m` from the slits where a bright fringe from one interference pattern coincides with a bright fringe from the other is

Options

A. 1.5 mm
B. 3 mm
C. 4.5 mm
D. 6 mm

Answer

C

Explanation

`y_(n) = n ((D lambda)/(d))` and `y'_(n) = n' ((D lambda)/(d))`
Equating `y_(n)` and `y'_(n)`, we get
`(n)/(n') = (lambda')/(lambda) = (900)/(750) = (6)/(5)`
Hence, the first position at which overlapping is
`y_(6) = y'_(5) = (6 (2)(750 xx 10^(-9)))/(2 xx 10^(-3)) = 4.5` mm