Dark and a Dot Where It's Not
The image of Saturn in eclipse taken by the Cassini spacecraft (above) made me start to think about things occult. No, not the "occult" as in astrology or fortune telling. The word occult means "hidden". It's a word used in astronomy when one object covers another. When the Moon covers the Sun, we call it an eclipse but it is also an occultation. If you were on the Moon during a Lunar Eclipse you could think of it as the Earth occulting the Sun. From the viewpoint of an astronaut on the Moon, a Lunar Eclipse would look very much like that view of Saturn from Cassini. The Earth would be a dark spot surrounded by a ring of sunlight from every sunrise and sunset happening at that moment.
Gedunken experiment time. Think about a magnifying glass. The lens is a disk of glass or plastic that is thickest in the center and smoothly tapers to a thinner edge. If light from far away, as from the Sun, goes through the lens, all the light tapers in a cone to a single point -- the focus. (This is where you rotten kids fry ants!) After all the light crosses at the focus point, it keeps going and makes another cone; this one getting bigger and bigger. Have you got that all pictured in your mind? Here comes the fun part. Imagine that your lens is 50mm in diameter (about 2 inches). Cut a circle of black paper 40mm in diameter and glue it to the middle of you lens. What happens now when you shine light through? The 5mm ring of the edge of the lens still lets light through and it still tapers in a cone to a focal point but, since no light gets through the 40mm paper disk, the cone of light is "hollow". If you put a white card somewhere behind the lens you would see a ring of light that gets smaller and smaller as you get closer to the focal point. Remember, this happens /on both sides/ of the focal point. Got all that? Now imagine putting a (dead) ant on a piece of glass right at the focal point and using some other light source than the Sun. (We're not trying to fry it now!) Put your eye on the other side of the glass with the ant on it and look back towards the lens. What will you see? Well, you will see the ant very nicely lit by the ring of light but beyond it you will see nothing but black because the black paper on the lens blocked that light. This is a very useful way of lighting small objects and microscopists (people who use microscopes) call this "dark field" because the field or background is black.
OK, you are back 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. The bright ring is clear (our atmosphere) and is thicker near the Earth and tapers to thinner -- just like the dark-field setup above! Yup, the Earth (and any other planet with an atmosphere) acts just like a big lens! The Moon is too close to us but if it were exactly at the focal distance of our "Earth-lens", the Moon would actually get brighter at the time of "eclipse"! The Moon would be the "ant" in our huge dark-field microscope! Here's the last nifty bit. 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!
Well, that's a nifty idea. Every planet with a clear atmosphere acts like a lens. Too bad for planets with no atmosphere, right? Well, let me introduce you to a little jewel in optics we call *defraction*.
When light is "bent" by a transparent medium (glass, plastic, or our Earth's atmosphere), we call that *refraction*. So telescopes with lenses are called refracting telescopes.
When light "bounces" off a shiny surface we call that *reflection*. If the shiny surface is curved like the inside of a bowl, the light bouncing off it can form an image. We call telescopes that do this reflecting telescopes.
Have you ever made a pin-hole camera? A pin-hole camera makes an image without using a lens or a mirror. Every time light (or any kind of waves) hits a sharp smooth edge, some of the light as it goes past the edge gets bent towards the edge and some of the light going past the edge gets bent away from the edge. We call this bending *defraction*. If the sharp edge happens to be a circle, the light that gets bent away from the edge focuses and forms an image just like a lens! We call telescopes that do this defracting telescopes. (There is a bit more to this idea but that will be in the next lesson.)
Remember that half the light that defracts from a sharp edge gets bent towards the edge. In a pinhole camera we don't use this light and it just degrades (fogs) the picture. Now here's the interesting part. Imagine that, instead of a pin-hole in a piece of opaque material, you have a sheet of clear, flat glass with a perfectly round black spot painted on it -- a reverse pin-hole. You guessed it; you can use this "fly spec lens" to make pictures just as you can with a pin-hole!
Well, we've been talking like a defracting imaging system has to use a tiny pin-hole (or black dot). It turns out that /any/ circular hole or dot will make an image -- the bigger the hole the longer the focal length. So if you can make all the windows in your classroom opaque (with thick cardboard or aluminum foil or something) and make a perfectly round smooth hole about 3" in diameter in the center window cover, (your "pinhole"), you will project an (upside-down & backwards) image of everything outside on your classroom wall opposite the widows. You will be sitting inside a "camera obscura".
So if you have a planet without an atmosphere, it will still act like a huge "fly spec" defracting lens. If you are on a moon orbiting that planet at the exact correct focal length distance of this huge, planetary defracting lens, again, just like we saw before with a planet /with/ an atmosphere, when your moon goes into eclipse it get brighter from the light defracted around your planet and if you look back at your planet it will seem to have a bright spot in the middle. This is called a "Poisson spot", named for Simeon Denis Poisson. In 1818, Augustin Fresnel (more about him later) presented the mathematics to demonstrate that light was a wave. Poisson thought this was ridiculous because, if true, there would be a bright spot in the back of a sphere when illuminated from one side. Dominique Francois Arago thought it would be easy to test and, sure enough, there was the spot! I think it should be called the Arago Spot! Sometimes science history just isn't fair.
All round opaque objects, planets included, whether or not they have an atmosphere, will act like a huge lens because of the refractive and defractive nature of light. There is more to the story than that.
Remember way back when we talked about Einstein's General Theory of Relativity (above)? One of the tests for the General Theory of Relativity was to see if starlight was bent by the gravitational attraction of the Sun (it was). Now gravity is really, really weak. Usually we only talk about gravitational lensing with objects at least as big as a star but planets (ok, /everything/) do also bend light. The focal length of the gravitational lens of a planet is very, very long but you still get that brightening at eclipse that we also saw with refractive and defractive planetary eclipsing. Astronomers use this brightening to search for planets in very distant star systems.
There you have it. Every planet is a lens and has 2 or 3 different focal lengths! Maybe someday we will find a planet made entirely from nice clear ice or diamonds then we will have another way of bending light on a planetary scale.