In a double slit experiment the distance between the slits is d. The screen is at a distance D from the slits. The order of the fringe which appears opposite to the slit on the screen is

$d^2/2λD$ $2λD/d^2$ $d/λD$ $2d/λD$

$d^2/2λD$

The position of the bright fringe is opposite to the slit, hence d/2 must be equal to integral multiple of the fringe width (λD/d). Thus $\frac{d}{2}=n.\frac{λD}{2}$ $⇒n=\frac{d^2}{2λD}$