A double-slit calculator

You will write three functions for Young's double slit.

The idea. The fringe width is $\beta = \lambda D/d$. The $n$th bright fringe is at $n\beta$ from the centre. The $n$th dark fringe is at $(n - \tfrac12)\beta$, counting the dark fringe nearest the centre as the first.

Your tasks.

1. In fringe_width, return $\beta$ in mm for a wavelength in nm, a slit distance d in mm and a screen distance D in m.
2. In bright_position, return the distance in mm of the nth bright fringe from the centre.
3. In dark_position, return the distance in mm of the nth dark fringe from the centre.