[Physics] Calculating total number of fringes in Young’s Double Slit Experiment

Question

I know that the $n^{th}$ order maxima can be given by $\frac{n\lambda D}{d}$. But theoretically n can go up to infinity and the intensity will go down. However, is there any way to approximate the visible bright spots that can be observed in experiments?

Answer 1

In Young's slits, the two beams that interfere have a width limited by the diffraction by the slits. The fringes are visible only in the common part of the two beams.

By neglecting the distance between the slits, the angular width associated with the diffraction is $2(\lambda /a)$and the angular width of a fringe is $\lambda /d$

As the central fringe is bright, we will roughly have $N=1+2d/a$ visible fringes. It is an approaching reasoning that may forget certain elements!

Sorry for my poor english !