A light source, which emits two wavelength `lamda_(1)=400nm` and `lamda_(2)=600nm`, is used in a Young's double slit experiment. If recorded fringe width for `lamda_(1)` and `lamda_(2)` are `beta_(1)` and `beta_(2)` and the number of fringes for them within a distance y on one side of the central maximum are `m_(1)` and `m_(2)` respectively, then

Options

A. `beta_(2) gt beta_(1)`
B. `m_(1) gt m_(2)`
C. From the central maximum, 3rd maximum of `lambda_(2)` overlaps with 5th minimum of `lambda_(1)`
D. The angular separation of fringes for `lambda_(1)` is greater than `lambda_(2)`

Answer

D

Explanation

`beta = (lambda D)/(d) rArr beta_(2) gt beta_(1)` `(because lambda_(2) gt lambda_(2))`
Also, `m = (y)/(beta) rArr m_(1) gt m_(2)`
3rd maxima of `lambda_(2)` lies at `3 (600 nm) xx (D)/(d)`
`= (1800 nm) (D)/(d)`
5th minima of `lambda_(1)` lies at
`(2 xx 5 - 1), (400) xx (D)/(d) = (1800nm)(D)/(d)`
Angular separation is `(beta)/(D) = (lambda)/(d)`
`rArr` It is more for `lambda_(2)`.
Therefore, choice (d) is incorrect.