Consider a usual set up of Young’s double slit experiment with slits of equal intensity as shown in the figure. Take ‘O’ as origin and the Y axis as indicated. If average intensity between $y_1=\frac{λD}{4d}$ and $y_2 = +\frac{λD}{4d}$ equals 'n' times the intensity of maxima, then 'n' equals

$\frac{1}{2}(1+\frac{2}{π})$

Phase difference corresponding to $y_1 = -π/2$ and that for $y_2 = +π/2$

∴ Average intensity between $y_1$ and $y_2$ = $\int\limits_{-π/2}^{π/2}\frac{I+I+2\sqrt{II}\cos \phi d\phi}{π}$

$=\frac{2I}{π}\int\limits_{-π/2}^{π/2}(1+\cos \phi)d\phi=\frac{2I(π+2)}{π}$

$I_{max}=4I$

∴ The required ratio = $\frac{1}{2}(1+\frac{2}{π})$