Question

White light falling on two long narrow slits emerges and is observed on a distant screen. If red light (680 nm wavelength) in the first-order fringe overlaps violet in the second-
order fringe, what is the latter's wavelength?

Answer 1

The angular position of the mth fringe is given by the following for small angle

a$\Theta$1 = m$\lambda$

but

a$\Theta$1(red) = 1$\lambda$red

a$\Theta$2(violet) = 2$\lambda$violet

$\Theta$1(red) = $\Theta$2(violet) ------i.e fringes overlap

$\lambda$red = 2$\lambda$violet

$\lambda$violet = $\lambda$red/2 = 680 nm / 2 = 340 nm