Single Slit Diffraction

The discussion of two slits as two coherent sources of is conceptually easier. Nevertheless, a single wider slit results in a simpler interference pattern which is also present in the double slit experiment. Implementing Huygens principle yet again, we treat every point in the continuous opening of the slit as if it were a singular source of light.

Here we can see a planar wave arriving at an opening in an opaque obstacle (what we call a slit). The wave at the opening acts a a collection of source points which propagate through the slit.

Even the seemingly negligible interaction with the edges of the slit produce an interference pattern due to the diffraction of the wave on them. In analogy to the geometric analysis performed in the double slit experiment we can draw the following diagram

And produce an equation that ties the wavelength of the incident beam and the dimensions of the system (slit width and distance from screen) to the density of the bright patches of constructive interference on the screen

which is functionally the same result as in the double slit experiment, with the slit width b in place of the slit separation d. We can also present the result of the Franhaufer diffraction integral for the single slit which presents a more complete picture of the intensity

where the sinc function is defined as follows

We care about the intensity since it is what we actually see with our eyes

In the double slit post we discuss how the double slit pattern contains the single slit pattern as is apparent in the above figure.