In YDSE, if a bichromatic light having wavelengths `lambda_(1)` and `lambda_(2)` is used, then maxima due to both lights will overlaps at a certain distance y from the central maxima. Take separation between slits as d and distance between screen and slits as D. Then the value of y will be

Options

A. `((lambda_(1) + lambda_(2))/(2D))d`
B. `(lambda_(1) - lambda_(2))/(D) xx 2d`
C. LCM of `(lambda_(1) D)/(d)` and `(lambda_(2) D)/(d)`
D. HCF of `(lambda_(1) D)/(d)` and `(lambda_(2) D)/(d)`

Answer

c

Explanation

Let `n_(1)^(th)` maxima corresponding to `lambda_(1)` be over lapping with `n_(2)^(th)` maxima corresponding to `lambda_(2)`. Then, the required distance
`y = (n_(1) y_(1) D)/(d) = (n_(2) lambda_(2) D)/(d)`
= LCM of `(lambda_(1) D)/(d)` and `(lambda_(2) D)/(d)`