In the Fraunhofer diffraction pattern of a double slit it is

Solution

Condition for missing order is

(e+d) /e = n/ m

Where e = slit width

            d = slit separation

If this condition is satisfied then n th order is absent.

According to problem , fourth order is absent.So, n = 4m.

Substitute this valur in above equation you get ,

(e+d) / e = 4m/ m

             = 4

   e+ d =4 e

        d = 4e - e

           = 3e

i.e., if the slit separation d is equal to three times the slit widththen 4 th order is missing.

Therefore the ratio of slit width e to slit separation d is e / d = 1/ 3