How to Spot a Psychopath

A reader writes:

Here's an interesting science question (for me at least!).

I've often observed a phenomenon. In sunlight - especially early or late when the sun is low and the rays come low - you can play with shadows on fairly distant objects (few meters); this seems essential for the effect.

The effect itself: If you move your fingers close to each other, while the sun shines through between them, as you close the gap between the fingers, the shadow of your fingers seem to stretch out and touch well before they actually touch. (Of course you don't have to use fingers, you can use something else.)

It's weird, really weird.

Steve

The sun isn't a point source of light; like most light sources, it has a clearly visible diameter. All shadows from it are, therefore, fuzzy to a greater or lesser extent, depending on how close the shadow-casting object is to the surface on which the shadow is cast.

A fuzzy shadow has an "umbra" and a "penumbra". The umbra is the evenly-dark portion of the shadow; if you're standing in the umbra, you can't see the light-source at all. The penumbra is the portion around the umbra which is partially shadowed. If you're standing in the penumbra, you can see some, but not all, of the light source's area. The closer you are to the umbra, the less of the light source you can see.

The umbra and penumbra distinction is particularly important if you're trying to get a good view of a solar eclipse; in a partial solar eclipse, the moon never covers the whole disc of the sun. You can see this in that famous picture of a solar-eclipse shadow viewed from low earth orbit, and it's diagrammed, rather less beautifully, here:

(Note also the "antumbra", which you see if you're far enough from the shadow-casting object that you see the light source all around it. This illustration's good, too. In a lunar eclipse, the moon is covered by the earth's shadow; a lunar eclipse is partial if the moon is never completely covered by the umbra of the earth-shadow.)

Now let's get back to the shadows of your fingers when you're doing Deformed Rabbit in late-afternoon sunshine. The shadow of each of your fingers, when it's cast by a light with considerable angular size like the sun or a much closer, much smaller light source like a light bulb, also has an umbra and a penumbra. Where two finger-shadow penumbrae overlap, an ant squinting up from the overlap area would see one side of the sun obscured by one of your fingers, and the other by another finger.

Result, a darker shadow, as the penumbrae add up. As you've noticed, this makes it look as if the shadows are stretching toward each other.

(You don't see this effect very much with most household lighting, because most people don't paint their rooms matte black and light them with a single dangling frosted bulb. Uneven illumination escaping from a lampshade, and indirect light bouncing off the ceiling, make normal indoor lighting quite unlike sunlight on a clear day, even if there's only one light source in the room.)

Freaky shadows can also be caused by diffraction effects, but with a wide light source and relatively large shadowing objects, you won't see them. If you've got a really really tiny light source with, preferably, a very tightly limited spectral output, though, all shadows will be super-sharp (with invisibly small penumbrae), and diffraction effects spring into visibility.

You can get such a light source if you unscrew the collimating lens completely from a laser diode module; this is possible with many, but not all, cheap laser pointers. Now you've got a narrow-spectrum light source about the size of a bacterium to play with!

Psycho Science, as I have brilliantly decided to call it, is a new regular feature here. Ask me your science questions, and I'll answer them. Probably.

And then commenters will, I hope, correct at least the most obvious flaws in my answer.