Notes from Under Sky

What Price Power?

Where does the 50x per inch limit on magnification come from?

D. Loolberman wrote:

I am looking (isn't everyone) for a scope. I am seriously considering the 10" starfinder EQ. On astronmics website they have it listed along with some tidbits of info. One tidbit says highest useful power = 228x. I did the math (focal length (1140mm)/eyepiece = power (228x)) and turns out to be a 5mm EP to reach 228x. Does this take into consideration a barlow for 2x or 3x? What happens if you place a 5mm into a 2x barlow, does this equal 456x or is my math wrong? Would it be outrageous and very newbie of me to try and get magnifications of 300x to 400x in a 10" scope on the planets? I know that seldom conditions are good enough to use these powers but, I do not want to buy a scope that limits me.

A decent 10-inch telescope should easily be able to exceed 228x, should the atmosphere permits it. The commonly stated limit of 50x per inch of aperture would yield 500x, well above 228x. But, I would say that this limit, and what yields it, is one of the most poorly understood areas in amateur astronomy.

Now, a little background information. Why 50x per inch? Why not 100x per inch, or 200x per inch, if the optics are good enough? Is it some kind of engineering limitation? No. The very nature of light itself creates an unavoidable blurring in the image, and this blurring is magnified right along with everything else. At some point, in fact, you will see blur and very little else.

What is the size of this blur? Informally, it is enough to consider the size of the so-called Airy disc. The Airy disc is what a singular point of light looks like, when viewed through a telescope. After passing through the optics, that point of light is no longer a point, but a small disc. That is due to the diffractive nature of light.

I'll use my own 5-inch scope as an example. The width of the Airy disc is measured in angles, not in inches or mm. The angular width of the disc in my 5-inch scope is about one arcsecond—that is, 1/3,600 of a degree, and about 1/1,800 the width of the full moon. So it's a very small angle indeed.

However, once you magnify that disc 250x—which is the 50x per inch "limit" on my telescope—that blows up to about 1/14 of a degree, and 1/7 the width of the full moon. I think you can convince yourself that it's quite easy to see a disc that's 1/7 as wide as the full moon—about 4 arcminutes, for those of you scoring at home. So, at that point, it's considered pointless to magnify further. As a matter of fact, since most eyes can discern detail down to perhaps 2 or 3 arcminutes, you can get all the detail at lower magnifications, like 150x or 200x, which is 30x or 40x per inch.

What about your 10-inch telescope? You might guess that a telescope twice as large would create an Airy disc that is also twice as large, but that's not the case at all. In fact, it's the exact opposite: the Airy disc becomes half as large. Therefore, it takes twice as much magnification to make the Airy disc as large as it was in the 5-inch telescope. So, where the limit was 250x in the 5-incher, it's now 500x in the 10-incher, and the limit grows larger in proportion with the aperture. That's why that limit is often expressed in power per inch of aperture.

Sometimes, the atmosphere provides so much blurring on its own that the telescope is no longer diffraction-limited (that is, limited by the width of the Airy disc). Instead, it's atmosphere-limited, and that limit does not get better as the aperture increases. If anything, it gets worse. The larger your telescope, the rarer are the occasions on which your observing is diffraction-limited.

However, at those magical times when the atmosphere is perfectly steady, the 10-inch telescope will handily outperform the 5-inch telescope, no questions asked. (It'll beat it most times, but the difference becomes smaller as the atmosphere gets worse.) Now, I said before that sometimes you can see all the detail you can at perhaps 30x or 40x per inch. And if your eyes are really good, and you can see down to one arcminute of detail, perhaps you can get it all at 20x per inch. Why, then, would you bother with 50x per inch at all?

Well, because it's not just about seeing it at the lowest power possible. Sometimes, the detail is just easier to see at higher power. If you can see it at 20x per inch, great for you, but perhaps it's a strain on your eyes to see detail at your limit. Better to magnify it twice as much, say, and make it easier to see. After all, we sit on chairs and cover our off-eye to reduce muscular strain, why not add extra power to reduce visual processing strain? And if your eyes aren't so acute, you need the extra power to see the details.

What's more, aberrations in your eye such as astigmatism are more acute at the edge of your cornea and lens than they are in the center. Using extra power shrinks the exit pupil of the image so that it all fits in the center of your eye, sometimes improving the quality of the image, especially if you have considerable astigmatism.

The only concern about overmagnification is that at some point the noise in the image—caused by atmospheric turbulence, defects in the scope, and the diffractive nature of light—overwhelms the flattened-out signal. Experience tells us that that happens somewhere near 50x per inch, but on high-contrast objects like the moon, sometimes the limit is closer to 100x per inch.

So, in conclusion, your scope should have no problem attaining 456x, if its quality, its tuning (collimation), and the atmosphere permit. I've heard that Meade mirrors are actually pretty good, so if you keep the collimation in tune, you only need to wait for the atmosphere to allow you to rack the power way up there. However, depending on where you live, that could be a very long wait.

Copyright (c) 2000 Brian Tung