# Single-slit diffraction

When light passes through a single slit, we still have an interference pattern. We can think of the slit as a set of many point sources. We get a bright antinode in the centre, and it has a width of $\displaystyle 2 \Delta{} y$. All the other antinodes are $\displaystyle \Delta{} y$ wide, and the brightness decreases rapidly as you move away from the centre:

The nodal lines in single-split diffraction occur when the path difference from the top and bottom points on the slit are $\displaystyle \lambda$, $\displaystyle 2 \lambda$, $\displaystyle 3 \lambda$, etc. The antinodes occur at $\displaystyle 0$, $\displaystyle 3 / 2 \lambda$, $\displaystyle 5 / 2 \lambda$, etc. This is counterintuitive, because a full wavelength of delay means that the waves arrive in phase and have constructive interference (which would be an antinode). However, when the path difference is $\displaystyle \lambda$, there is only one pair of points in the slit that result in this constructive interference. The others are all closer together, and there are many pairs of points separated by a half wavelength, which is destructive. The antinodes have a mix of constructive and destructive interference; this mix becomes increasingly destructive as you move away form the centre, which is why the brightness goes down.