Light waves in interference?

Question

Light with wavelength 422 nm passes through a double-slit system that has a slit separation d = 0.400mm.Deter-mine how far away a screen must be placed so that dark fringes appear directly opposite both slits,with only one bright fringe between them.

Answer 1

The small-angle approximation says y/D = λ/d, so D = dy/λ.
(It's a case of nearly-similar triangles.)
If y = d = 0.0004, then D = 0.0004^2/422E-9 = 0.379 m
Note y is the distance between adjacent minima or maxima. See the ref. for excellent explanation.