Can we see through the central obstruction of a lens?

I have a very basic question in optics inspired by this article from the University of Stanford which clearly states that one should see a light source through a mask in the middle of a lens if the observer is at the focal point:

OK, you are on the Moon during a lunar eclipse. Look back at the Earth. To your eye, the Earth is a black disk with a bright ring around it. [...] Yup, the Earth [...] acts just like a big lens! [...] If you were on the Moon and the Moon was, indeed, at the focal point of our Earth-lens, when we looked back at the Earth you would see the bright ring around the black circle of the Earth but there would also be a bright spot smack dab in the middle of the black disk of the Earth. This spot is the focused light of the illuminated ring of atmosphere. Got it? Shiny!

To test this, I have bought a magnifying glass and put a mask (an obstruction) on it that is half the size of the lens. I have a light source point placed at infinity along the optical axis and, as expected, an image of it (another light point) at the focal distance on the other side of the lens. Then, I have placed my eye at the exact position of this image point and looked toward the lens. I think I re-created exactly the setup presented in the article.

First, I was happy to see that the annular lens around the mask looked uniformely lit by the source point located behind, as described by the article. But while I expected to see the point "through" the mask, the mask was just... blocking the light and there was absolutely no bright spot in the middle. My question is simple: why can't we see the point in the middle of the blocking mask when our eye is located at the focal point ? Am I wrong, or is this article wrong ?

• By the way, in the cited article, "defraction" is a painful misspelling of "diffraction". Also, if you try the experiment with an ant, the ant will be incinerated because there will not be a hole in the focused image. The hole appears only upstream and downstream from the focus. Be suspicious of an author who misspells important words from his own field. May 19, 2018 at 2:25

1 Answer

If you draw the rays you will see that, when your eye is at the focus, there are no rays entering your eye in line with the center of the lens (and with the point source). Rays from the source are approaching the focus from all directions, and thus approaching your eye from all directions. You can only see a point source at infinity if the rays are parallel.

If you were expecting to see the point source at the focus when you put your eye there, that (as you discovered) doesn't work either. In essence, the lens forms an image of the point source at the lens focus. If you put your eye at the focus, it's like putting your eye on the point source, and your eye just can't focus on something that close.