White light (400 nm to 800 nm) is used in YDSE, where D = 0.5 m, d = 1 mm. Find the missing wavelengths in front of one of the slits on screen?

$\Delta x=\frac{dy}{D}=\frac{d}{D}\left(\frac{d}{2}\right)=\frac{d^2}{2D}$

$\begin{array}{l}(2n-1)\frac{\lambda }{2}=\frac{d^2}{2D}\\ \lambda =\frac{d^2}{(2n-1)D}=\frac{{10}^{-6}\times 2}{(2n-1)1}\end{array}$

$\lambda =\frac{2000}{(2n-1)}nm$

When n=1, 2000 nm = l = (not possible because not in given range

When n=2, l =2000/3 nm

When n=3, l =2000/5 nm=400nm

${\lambda }_1=\frac{2000}{3}\&{\lambda }_2=400$ are the missing wavelengths