"These lovely lamps, these windows of the soul" — to 16th-century poet Guillaume de Salluste, the eyes revealed a person's inner being. The rest of us look into the pupils of the eye and see only impenetrable blackness — but look out through them, and there's the world in all its sadness and glory. An astronomer looks at them and sees optical parts that need to be mated properly to any other optical instrument being employed, such as a telescope or pair of binoculars.

Understanding pupils is important for skywatchers who want to know which telescope eyepieces or binoculars to buy. It is also the key to some relatively unknown aspects of visual observing.

Pupils come in two types. The entrance pupil refers to the aperture through which light enters an optical instrument such as a telescope. The exit pupil is a small circle just behind a telescope through which all emerging light rays pass. You can see it as a little disk of light floating in the air behind the eyepiece when the instrument is pointed at a bright surface, such as a wall or the daytime sky. This disk is an image of the telescope's aperture. Its size equals the aperture divided by the magnifying power.

The size of the exit pupil is crucial because it must fit into the pupil of your eye (I explain why below). This simple fact governs your choice of optical systems. In practice, however, the matter is not always as simple as it seems.

For one thing, your eye's pupil shrinks in bright light and expands in the dark. Just how big it can get under a starry sky is the subject of much misunderstanding. The ancient dogma on this topic, printed in countless books, says "The human pupil dilates to a maximum diameter of 7 millimeters." Therefore 7 mm is supposed to be the ideal maximum size for the exit pupil of binoculars or a telescope.

This is the reasoning behind the popular 7x50 "night glass" binocular. Divide its 50-mm aperture by its 7-power magnification and you get an exit pupil 7.1 mm across, just about right.

But it ain't necessarily so. Everybody is different.

Some of us have night-owl pupils that enlarge to nearly 9 mm in the dark; others don't make it to 4 mm. After young adulthood there's a gradual downward trend with age — slowly at first, then more rapidly from about age 30 to 60, then slowly again in your later years. But even among people the same age there's a good 3 mm of scatter, so that some 70-year-olds outdo some teenagers.

The problem is that if the exit pupil of a binocular or telescope is too large to fit into your eye, you lose some of the instrument's incoming light. Imagine your eye's greatly magnified iris covering a telescope's front end like a prop in a horror movie, diaphragming the instrument down to a smaller aperture. For example, when a 4-inch (100-mm) telescope is used at 10x, its exit pupil is 10 mm across. If your eye's pupil is only ¾ this size, you're only looking through ¾ of the telescope's aperture — it's acting as a 3-inch, not a 4-inch. Clearly, 10x is too low a power to use on a 4-inch telescope if you want to take advantage of its full light-gathering abilities.

Similarly, if you're in late middle age and have a maximum pupil size of only 5 mm, your 7x50 binoculars are acting as 7x35's, and those big 10x70s you've been thinking of buying might as well be 10x50s.

The same goes for telescope eyepieces. If you have a 5-mm eye pupil and an 8-inch (200-mm) telescope, you should use no less than 40x. In all cases, the lowest power that allows full use of the aperture equals a/p, where a is the aperture and p is your eye pupil size.

Or to state it a different way: If you have a 5-mm eye pupil, you cannot use an eyepiece longer than 20 mm focal length on any f/4 telescope, or 30 mm on any f/6 scope, if you want full use of the aperture. This is true regardless of the telescope's size or anything else. The rule here is e = fp, where e is the eyepiece focal length, p is pupil size, and f is the telescope's f/number (focal ratio).

Clearly, "know thy pupil size" should be the watchword when buying. Two ways to measure your pupil are described at the end of this article.