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I am thinking about making a telescope. I have a 100cm focal length lens which I can use as objective lens in my telescope. So which is the best focal length I can use as eyepiece in my astronomical telescope?

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  • $\begingroup$ What do you want to look at specifically? Distant stars and galaxies or planets within our solar system? $\endgroup$ – CipherBot Nov 6 '15 at 1:49
  • $\begingroup$ I want to see planets and stars.Mainly I want to see planets $\endgroup$ – user213892 Nov 6 '15 at 11:48
  • $\begingroup$ Can you tell us the size (diameter) and nature of the objective? $\endgroup$ – Conrad Turner Nov 6 '15 at 12:59
  • $\begingroup$ Objective is a 50mm diameter convex $\endgroup$ – user213892 Nov 6 '15 at 14:26
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The first question anyone asks about a telescope is "what is the magnification?" It is almost always not the most important thing. Any telescope can magnify a million times, given a short enough eyepiece - the problem is, how good the image is.

For observing planets, the main thing is resolving power - the ability of the telescope to discern tiny details. The resolving power is limited by aperture, or the diameter of the primary lens or mirror. If the primary lens diameter is measured in mm, and the resolving power in arcseconds, then the limit is:

resolving power = 100 / aperture

Your 50 mm diameter lens would have a resolving power limited to 2 arcseconds in ideal conditions. Any details smaller than that would be blurry, no matter how much magnification you put into that thing. For comparison, Jupiter's apparent diameter is between 30 and 50 arcsec, Mars' between 3.5 and 25 arcsec, Saturn's between 14 and 20 (without the rings).

With that aperture you would see the rings of Saturn, and a couple equatorial belts on Jupiter. Venus shows a crescent when it's far from the Sun. Mars is a little orange disk when it's closest to Earth. I've looked at planets through 50 mm of aperture, and you can see quite a few things that way.

The Moon also looks interesting, you can see craters and mountains, plus it's available every month.


Because resolving power is limited by aperture, as you give it more and more magnification, at some point the image is just huge and bloated; big, but blurry. So there's a limit to the useful magnification - again, this depends on aperture. If the aperture is measured in mm, the formula is:

maximum magnification = 2 * aperture

Your 50 mm aperture would support up to 100x magnification before things get too blurry.

So how do you calculate magnification for a given instrument? It is the ratio between the focal length of the primary lens (or mirror) and the focal length of the eyepiece (the lens close to your eye):

M = F / f

For your 1000 mm focal length primary, you achieve 100x magnification with an eyepiece with 10 mm focal length. Anything shorter than that would just bloat the image uselessly. Eyepiece focal lengths that would make sense in your instrument would be between 10 mm and 120 mm.


Words of advice:

Make sure the lenses are perfectly aligned. When you build the instrument, have some way to adjust the direction of the primary lens, so as to align it with the main axis of the instrument. Some tweaking will be required - tilt the primary a fraction of mm, check the results, tilt again, repeat until the image looks best. This is called collimation and it's very important for the overall performance of the instrument.

Have some way for the eyepiece to move back and forth until you achieve perfect focus. This will have to be re-adjusted every time you observe. The adjustment is quite sensitive. A real focuser would help a lot, but this could be achieved also with two tubes sliding into each other, held in place by friction, like in an old pirate captain's telescope.

For astronomy, when the scope is focused at infinity, the distance between primary lens and eyepiece is the sum of their focal lengths. E.g. with a 1000 mm primary and a 10 mm eyepiece, the distance would be 1010 mm. This assumes a convergent eyepiece.

The telescope will not work well hand-held. The image will be jumping around too much. You will need some kind of mount. At the very least put the top of the tube on a fence or something. But astronomical instruments work best when they are on a rock solid mount. Even a broomstick hammered into the ground, with a loop on top for the tube, is better than nothing.

Whichever way you mount the primary lens, don't squeeze it too hard in the lens cell or tube. It will deform the lens and make the image bad. Some pressure on the edge is okay; lots and lots of pressure not okay. You could glue the edge of the lens on some kind of ring. Just use common sense.

This is totally doable. I've built a telescope just like that, many years ago. It's great to see what you can achieve on your own.

Good luck!

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  • $\begingroup$ Thanks...but Can I be able to see Saturn's ring using 100mm focal length eyepiece.And does the diameter of eyepiece matters? $\endgroup$ – user213892 Nov 7 '15 at 1:50
  • $\begingroup$ A 100 mm eyepiece would provide about 10x magnification. I've looked at Saturn at 10x; if the scope is collimated it looks a bit like a very tiny letter phi: Φ. But for planets you want more magnification than that. Over 50x it becomes pretty clear what's going on. The diameter of the eyepiece would require a more complex discussion about field of view and aberrations; anything that's 10 mm in diameter or more should be very usable, but even a very small lens could get you started. 2" eyepieces have field stops up to 46 mm; any diameter much bigger than that would probably be pointless. $\endgroup$ – Florin Andrei Nov 8 '15 at 1:44
  • $\begingroup$ I should add that you could probably use just about any old eyepiece from a telescope, microscope, or binoculars. If it's from an old instrument, you could probably get it for free, and it would definitely outperform any single-lens eyepiece you could make. Use a single-lens eyepiece if you want to keep it simple, or if that's all you have for now, but keep an eye out for old instruments. Optics don't go bad in time if they are stored well. In time you could build up a collection of eyepiece lenses, giving you a range of different magnifications - that's what most people do eventually. $\endgroup$ – Florin Andrei Nov 8 '15 at 1:49
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There are a few rules of thumb you will need: Maximum useful magnification $M_{max}\approx D\times 50$ where $D$ is the diameter of the objective is in inches, and magnification $M=l_{obj}/l_{eye}$, where $l_{obj}$ and $l_{eye}$ are the focal lengths of the objective and eye piece respectively.

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  • $\begingroup$ Which is the minimum magnification for seeing planets clearly $\endgroup$ – user213892 Nov 6 '15 at 11:51
  • $\begingroup$ That depends on a lot of things, not only image size but contrast, but to get say the image of Jupiter (30-50 second of arc without magnification) up to something like 10 time the resolution of the eye (resolution of the eye ~0.5-1 minute of arc, so 5-10 minutes of arc) would require a magnification of something like 10 to 20, though you might well be better off with double that or more. As a reference: the Moon without magnification has an apparent size ~30 minutes of arc. $\endgroup$ – Conrad Turner Nov 6 '15 at 12:55
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The minimum focal length of eyepiece u can with your 50mm lens is fE = fO / DO that is, 1000 / 50 = 20 so, the eyepiece focal length for max magnification is f/20. fE = Eyepiece minumum focal length, fO = focal length of objective, DO = Objective daimeter.

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