White light is used to illuminate two slits in Young's double slit experiment. The separation between the slits is b and the screen is at a distance d( b) from the slits. At a point on the screen directly in front of one of the slits, which wavelengths are missing?

Step-by-step solution

The situation is shown in the figure The path difference between the waves reaching the point P is aligned p & =B P-A P & = (d^2+b^2 )^ 1 / 2 -d=d (1+ b^2 d^2 )^ 1 / 2 -d & d [1+ 1 2 b^2 d^2 ]-d= b^2 2 d aligned For a dark band p= b^2 2 d =(2 n-1) 2 where, n=1,2,3 or = 1 (2 n-1) b^2 d Hence, the missing wavelengths are b^2 d , b^2 3 d , b^2 5 d ,....