# What happens to the diffraction pattern of light as an aperture becomes infinitely small?

Will the point source according to Huygens principle start radiating backwards with nothing to cancel it out?

Will it be a complete sphere if light passes through an infinitely small aperture?

• – Ben Crowell May 1 '18 at 19:48

The Interference pattern behind an aperture in the far field is given by the Fourier transform of the aperture function. In the case of a 1-dimensional aperture, if the width of it is $d$, then the diffraction pattern is given by the function $$g(x)=\frac{\sin(x d)}{x} ,$$ where $x$ is the point on the screen. So, as $d$ goes towards $0$, you could argue that the pattern is just becoming more and more constant, going outwards from the middle of the screen. Of course since you are letting less and less light through, you could argue that the intensity also tends towards $0$ everywhere.

According to Huygens principle an infinitesimally small aperture is a single source of spherical waves. So there is no interferece because there aren't other sources of waves. If you put a panel back the aperture, like in the Young experiment, you should see light on all the panel, of course the intensity of light decrease from the centre of the panel to its edges.

The diffraction pattern spreads wider and wider until eventually the slit becomes to small for a photon too pass through. If you're talking billions of photons as in a beam of light then as the slit gets smaller, more photons will be absorbed by the edges and reflected back. You would never have a complete sphere of light passing through. I don't understand your secondary questions.