In Young's double slit experiment, the slits are 2 mm apart and are illuminated with a mixture of two wavelength `lamda_0` = 750 nm and `lamda` = 900 nm. What is the minimum distance from the common central bright fringe on a screen 2 m from the slits where a bright fringe from one interference pattern coincides with a bright fringe from the other?

Explanation

`n_(1)lambda_(1) = n_(2)lambda_(2)`
`(n_(1))/(n_(2))=(lambda_(2))/(lambda_(1))=(900)/(750)`
D = 2m
d = 2 mm
Thus, we have
`(n_(1))/(n_(2)) = (6)/(5)`
`5^(th) and 6^(th)` fringes will coincide respectively. The minimum distance is given as
`X_(min)=(n_(2)lambda_(2)D)/(d)=(5xx900xx10^(9)xx2)/(2xx10^(-3))`
`= 4500 xx 10^(-6) = 4.5 xx 10^(-3) m`
`X_(min) = 4.5 mm`