Magnification and focal ratio

Understanding magnification and focal ratio 

How to calculate for small, amateur telescopes

Take a look at these three amateur telescopes in the picture on this page; it may not appear so at first, but all three are the same size.  No, really – let's take a closer look. These two telescopes have similar sized lenses; the tallest one at the top is 76 millimeters, and the middle, silver one is 70 millimeters. The green, short reflector on the bottom/right has a mirror of 76 millimeters, so they are all within 6 millimeters – or ¼ of an inch – in diameter of each other. Why does that matter?

Well when we talk about how “powerful” a telescope is, or can be, what we really mean is how much light it gathers. There is a reason why the Hubble Space Telescope has a large mirror (though it is considered "small" by most professional telescope standards today), and other ground-based telescopes are measured in meters. Larger aperture gathers more light, and that allows us to see - or in the case of professional, photograph - dimmer objects and increases the resolution of the optical instrument.  But let's not get too far into the weeds: We'll look at these three similarly sized telescopes to understand magnification first.

To determine magnification of a telescope, we perform a simple calculation. Take the focal length of the telescope in millimeters, and divide that number by the focal length of the eyepiece you are using. So for example, let's take our three telescopes and look at each, assuming a 20 millimeter eyepiece.

FL(aperture) / FL(eyepiece) = Magnification

The long, white 76 millimeter refractor has a 1200 millimeters focal length. So if we divide that by a 20mm eyepiece, the magnifcation is 60x. For our shorter, silver-colored refractor, it's focal length is about 600 millimeters, so dividing that by 20mm, we get 30x. And for the short, stubby little reflector, it has a focal length of just 300 millimeters, so dividing it by 20mm we get just 15x! And think about this for a moment: If we change to a 10 millimeter eyepiece, we see the change in magnification for each, but the RATIO of magnification doesn't change among the telescopes. We'll talk those ratios about that in a moment.  Check out these two charts that calculate the two different eyepieces for the different telescopic focal lengths:

  

But first, how does each telescope's length alter what we can SEE in each telescope different? Well, it actually changes it rather substantially. Look at this: In the long refractor, we would see only this much of the well-known Pleiades star cluster. That's not much; the field of view is only three-quarters of a degree, and the Pleiades is much larger than that. 

Moving to our mid-sized refractor, we can now see quite a bit more, just barely fitting the entire cluster in the field of view. 

But the reflector is where we can see much more; look at how this view frames the cluster nicely. So the lower magnification and shorter focal length with it's wider field of view can actually help us see more.

How does that work? It works by understanding a bit about focal ratios. Remember, all of those telescopes were nearly the same aperture, but different lengths. This time, if we divide the focal length by the aperture, we arrive at some different numbers, but these are fixed numbers for every telescope, and do not change. The long refractor is nearly 16 to 1, as we divide 1200 mm into the aperture of 76mm and arrive at 15.8 for an f-ratio, or about f/16 - quite a long focal ratio telescope. The mid-length refractor is a shorter f-ratio: 600 millimeters divided by 70mm is f/8.5. And the short little refractor has the shortest focal length of all: 300 divided by 76 is 3.9 or close to f/4 – f/3 to f/5's are definitely short f-ratio scopes.

So the longer f-ratio telescopes provide more magnification with the same eyepiece, but less field of view; this makes it easier to get high magnification for planets, but harder to see wide field views. Middle ones can still provide fairly high magnification, decent fields of view as well; no wonder many f/7 to f/10 instruments are popular. And short focal length telescopes provide the widest field of view, but the least magnification using the same eyepiece, though in larger apertures, the focal ratio tends to get faster so that tube lengths do not become unwieldy and difficult to use or mount..

Of course, we can get more magnification with shorter eyepiece focal lengths or using barlow lenses, and wider fields of view using other types of eyepieces; but that has to do with the way certain eyepieces work (link coming soon).