Astronomy Hacks

Measure Your Entrance Pupil Size

Use an Allen wrench to match your instruments to your eyeball.

Your pupils constrict in a bright environment to limit the amount of light that reaches your retinas. In the dark, your pupils dilate to admit as much light as possible as part of the dark adaptation process [Hack #11].Astronomers refer to pupil diameter as entrance pupil size because it determines how much of the light from a binocular or telescope can enter your eyes. Measuring your entrance pupil size when your eyes are dark adapted gives you a key piece of information to help you select binoculars and eyepieces that are best suited to your own eyes.

Maximum dilated pupil size varies with age and other factors. A child under 10 years of age may reach maximum dilation of 8mm or slightly more when fully dark adapted. A young adult’s entrance pupil may be as large as 7.5mm. As we age, our eyes may no longer dilate as fully as when we were young. By age 35 or 40, we may be limited to 6.5mm or less dilation, by 50 or 60to only 6mm or less, and by 80 to only 5mm. (This is not invariably true; some 60-year-old eyes can still dilate to 7mm, and some younger eyes cannot dilate to a full 7mm.)

For maximum light gathering, you want the exit pupils of your binocular and telescope to be no larger than the entrance pupils of your dark-adapted eyes. This delivers the maximum possible amount of light and allows you to see the brightest possible image. If the exit pupil of the instrument is larger than your entrance pupil, you waste light.

Tip

To calculate the exit pupil of a binocular, divide the objective size by the magnification. For example, a 7X50 binocular delivers an exit pupil of 50/7=7.1mm, while a 10X50 binocular delivers an exit pupil of 50/10=5mm.

To calculate the exit pupil of a telescope, divide the focal length of the eyepiece in millimeters by the focal ratio of the scope. For example, a 25mm eyepiece used in an f/5 scope delivers an exit pupil of 25/5=5mm, while a 35mm eyepiece in the same scope delivers an exit pupil of 35/5=7mm.

If your fully dark-adapted entrance pupil is 5mm, for example, it’s pointless to use a 7X50 binocular because it delivers a 7.1mm exit pupil. In effect, your 5mm entrance pupil stops down your 50mm objective lenses to 35mm. You could instead use a 7X35 or 10X50 binocular, either of which delivers a 5mm exit pupil that matches your entrance pupil, and the images would be as bright as those you see with the 7X50 binocular. Similarly, looked at solely from a light gathering perspective, it makes little sense to buy an eye-piece that has a focal length longer than the focal ratio of your scope multiplied by your entrance pupil. If your entrance pupil is 5mm, for example, the longest eyepiece you should choose for use with an f/5 scope is 5 x 5mm =25mm.

Tip

You may choose to buy a longer eyepiece despite the fact that it “wastes light” because that longer eyepiece provides a wider field of view. For example, Robert, whose entrance pupil is about 6.5mm, routinely uses a 40mm Pentax XL eyepiece in his 10” f/5 scope. That eyepiece provides a huge 8mm exit pupil, and in effect turns the 10” f/5 scope into an 8” f/6.3 scope. That doesn’t really matter, though, because Robert is seeing that larger field of view as brightly as it is possible for him to see it.

Your eye doctor can measure your fully dark-adapted entrance pupil for you, but you can also determine it for yourself. To do so, you’ll need a set of metric Allen wrenches. Allow yourself to become fully dark adapted, which may take half an hour or more. Look directly at a bright star, and hold one of the smaller metric Allen wrenches along your cheek so that the long portion crosses your eye parallel to and near the eyeball, as shown in Figure 1-4. Move the wrench up and down until it is centered on your pupil. You’ll see the star split into two stars, one on each side of the wrench. Substitute larger Allen wrenches until you reach a point where the star no longer splits, but is visible only as a single star on one side or the other of the Allen wrench. The size of that Allen wrench is the size of your fully dark-adapted entrance pupil.

If you observe frequently from a light-polluted site, repeat the experiment there. You may be surprised at the difference light pollution, particularly from nearby local sources, makes to your dark adaptation. For example, if your entrance pupil is a full 7mm at a truly dark site, it may be only 5mm at a brighter site. Your eyes operate on the same principles as any optical instrument. Light gathering ability varies with the square of the aperture. That means a 7mm entrance pupil admits nearly twice as much light (7² versus 5²) as a 5mm entrance pupil, which in turn means that you can see nearly one full magnitude deeper from the darker site [Hack #13].