math homework

Eeewww.

Just reviewing all the basic math calculations... Remember to treat everything in consistent units, millimetres or inches, whichever. The slash symbol (/) is used in these notes of course to mean divide or division.

One of the common ones people want to know. "What power is that?"

eyepiece power or magnification
= telescope focal length / eyepiece focal length

Simple calculation you can often do quickly, crudely in the field. E.g. 2000 mm SCT with a 25 mm eyepiece is 80x (or 80 times or 80 power).

Focal length of a telescope is fairly easy to calculate for a refractor but gets increasingly complicated with reflectors and compounds. Eyepiece focal length is hopefully printed or stamped on the ocular itself. You can't tell just by looking, in general.

When I started serious observing, I needed to know how much an eyepiece-telescope combination showed of the sky. It was startling to finally, accurately calculate it.

eyepiece true field of view
= eyepiece apparent field of view / magnification

Now this one can be a little tricky to do, especially with older eyepieces, where the information was not sometimes published. In modern times, an eyepiece company will tell you all the specs. E.g. a Tele Vue 9mm (focal length) Type 6 Nagler has an AFOV of 82 degrees (°). If used at 222x, then the TFOV is 0.37°. I.e. you're seeing less than ½ a degree of sky. That's a circle no bigger than the disk of the Moon.

If you cannot determine the AFOV of an eyepiece, you can compute it "backwards" by doing "drift timings" with your telescope (assuming you have all the other numbers and you're OK with doing some trig!). That's a discussion for another day.

There is another way to calculate TFOV but it requires you know the eyepiece field stop diameter size.

eyepiece true field of view
= ( eyepiece field stop / telescope focal length ) * 57.3

Another interesting number is exit pupil. That's the size of the light cone emitted from the eyepiece. If it is significantly large than your iris (taking into account your dark adaptation, age, and other factors), you might experience a degraded image. Conversely, an extremely small exit cone is simply hard to see. You have to bob and weave to catch the image.

exit pupil
= telescope aperture / magnification

Aperture is the size of the opening at the "front" of the telescope. Often this is simply the clear glass in a refractor or the size of the mirror in a reflector or compound.

You would calculate exit pupil values when eyepiece shopping to ensure you don't get something that's inappropriate for your telescope configuration and your visual acuity.

If you want to know the "speed" of your telescope, then you need the focal ratio number.

focal ratio number
= telescope focal length / telescope aperture

Simply put, how long is it compared to how wide. This is usually shown as f followed by a slash and a number, e.g. f/5. The classic 8 inch (203 mm aperture) telescope with a 2000 mm focal length is an f/10 'scope. If you have experience with SLR cameras and interchangeable lenses, then you know something of aperture and lens speed.

Years ago I built an Excel spreadsheet to crunch all these numbers. Then I redid that in my Psion Sheet application so I had all the numbers in my pocket.

Found a handy calculator (the TEC) on the web too. There are lots. But the TEC let's you load in a set of eyepieces vs. one at a time.