Circular Apertures and Resolving Power
![[url=https://pixabay.com/en/eye-iris-macro-natural-girl-2340806/]"Human Iris Pupil"[/url] by SofieZborilova is in the [url=http://creativecommons.org/publicdomain/zero/1.0/]Public Domain, CC0[/url]](https://www.geogebra.org/resource/Ra7GdZJA/EfsviEWM7oCGnThG/material-Ra7GdZJA.png)
Resolving Power
Pictured above is the most commonly used circular aperture on our planet - that of the eyeball's pupil. The black pupil at the center of the eye is literally a window to the dark interior of the eye, at the back of which is the retina. We've discussed this before. The part we have not discussed is the fact that it plays the role of a circular single slit, and has associated diffraction.
While you might rightfully argue that the pupil is rather large compared to the wavelength of light, and therefore shouldn't have much diffraction associated with it, that all depends on how we quantify "much". It turns out that the tiny bit of diffraction that the pupil does produce on the retinal surface, can be the limiting factor for a healthy eye's ability to see detail in things at a distance or at a small scale. What do I mean by this?
Imagine I have a checkered towel that I hold up for you to see. Then I tie it around my neck and drape it down my back as a cape and walk down the street looking like a super hero. As I walk away you watch me. There will be a distance at which you will no longer see the checkers, but rather will see the cape as single-colored with no pattern on it. The distance at which this occurs can depend on one of two things - one of them being the size of your pupils. This occurs because of diffraction. The bigger your pupils are, the farther I could walk before the checkers would blend together. We’ll talk in a bit about the other potentially limiting factor. But let’s focus on the diffraction first.
The ability to see things as distinct (the checkers) at a distance is spoken of differently in optics. Instead you say "I can resolve the checkers up to a distance of x", or "my eyes have less resolving power than a telescope".
There are conspiratorial websites that claim we never went to the moon. At times they will use as proof the fact that we can't see the flag even with a powerful telescope from here on earth. We will investigate how silly that line of evidence is once we establish the resolving power based on aperture size. While telescopes do have a much higher resolving power than human eyes, both the atmosphere and the size of a telescope's aperture (same as tube diameter, essentially) is a limiting factor.
I should also mention that resolving power isn't just about seeing things at a distance, but really relates to seeing any object with a small angular size. Imagine two pixels on the computer screen on which you're reading this. Can you see them? Get a bit closer. Now can you? Is there a point at which you can start seeing distinct pixels on your screen? Some screens these days have pixels spaced closer than the resolving power of a healthy eye allows to see while at the near point of 25 cm. Apple corporation called the first such screens "retinal screens". It is not clear to me whether they thought that the spacing between cone receptors on the retinal surface was the limiting factor or whether they were thinking of diffraction on the retinal surface, and I haven't looked into this question. The fact is that the two occur at very similar angles, but that the cone spacing is roughly two times denser (in most eyes) than that which could be justified by the pupil diameter. In other words, human vision is often diffraction limited in a healthy eye due to the pupil diameter. With larger pupils the limitation on vision (and resolving power) would be the cone spacing on the retinal surface.
We will discuss more details of human vision in this chapter.