The Big Think

July 26, 2007

Getting My Focus

Filed under: Telescope — jasony @ 9:54 am

I spent two hours last night reading and learning about optics and telescope mirrors. Took some good notes in my new leather journal Erin gave me a few months ago. It’s got a short leather strap that acts as a tie-up to close the thing. Very Henry(Indiana)-Jones looking.

I’ve always been confused by the relationship between focal length, mirror size, and f/ratio on telescope mirrors. Often designers and scope nuts go off on tangents on the benefits of an f/5 scope vs an f/8 or f/11 scope. I’ve never internalized what they mean by this so I quickly get lost when they start talking about it. I understand f/ratios when it comes to photography, but mirrors are a little different. So I decided last night to figure it out once and for all. And I did!

In a nutshell, the smaller the f/number (called the “f/ratio”) is, the shorter the telescope tube will be. What makes a smaller f/number? A more curved mirror. Think of it this way: if you have a flat mirror the light that hits it and bounces off will never come to a focus (f/infinity). Grind a little bit out of the center of the mirror glass, making it more curved, and the light rays will reflect off of it and meet somewhere far away from the mirror (lets say 100′). As you start to grind more and more material out of the mirror, making it more curved, the light rays will start to be focused to a common point that is closer to the mirror. Eventually, the mirror will be so curved that the reflected rays will focus, oh, about four feet away (just an example).

So let’s say you decided to stop grinding your 8″ mirror once the light rays focus four feet (48″) away. Congratulations, you have an f/6 mirror. Why? Because 48″ (the focal LENGH) divided by 8″ (the diameter of the mirror), is 6… so they would call your mirror an f/6.

It’s easy to grind a mirror without much curvature to it, but this will mean a really long telescope. For example, an 8″ mirror that focuses light 120″ away would be an f/15 mirror… and the scope would have to be 10 feet long! Remember, you have to actually look at the light at the point it all focusses together, which means some sort of secondary mirror or eyepiece at that focal point, which means a long telescope tube to support all that hardware. Much better to spend more time making the mirror more curved so you don’t have a behemoth of a telescope.

So why not keep grinding away until you have a bowl-shaped mirror that can focus, say, 12″ away? In this case, a 12″ focal length mirror that is itself 8″ in diameter would be an f/1.5 mirror. But you’ve taken off so much glass from the middle of the mirror that it is quite literally bowl-shaped. These extremely curved mirrors are not only hard to make accurately, but the can be weak in the center (flexing!) and they suffer from something called “spherical aberration”. Basically, the image won’t look very good because the light rays are bent so dramatically.

Most telescope makers/mirror grinders recommend a happy medium of around f/5 or f/6. So if you’ve decided on an 8″ mirror, you get a final telescope length of around 40-48 inches. I think I’m going to go with a 6″ mirror in mine because the raw materials are a little cheaper. An f/5 or f/6 mirror means the final tube length will be 30″ to 36″ long, or about three feet (5×6 or 6×6). I think this will strike a nice balance between size, ability, portability, and cost. A 6″ mirror ground to f/5 would cost around $150-200 if I purchase it outright. If I do it myself I’d pay about 1/3 that price. Of course, grinding a mirror can take 50 hours, so I’m not really “saving” that much. I’m still not sure if I’m going to grind it myself or buy. I’m not really to that decision point just yet.

But I have decided on a six inch reflecting telescope along the lines of this basic design:


Light goes in the front, reflects off the curved mirror, and converges at the secondary mirror where it is reflected to the eyepiece. It’s called a “Newtonian reflector” and is a good balance between capability and size. It’s also not too hard to build. Most Newtonians have round tubes that you can construct from- no kidding – cardboard cement tubes you buy at the hardware store. I may get a cardboard tube to test the optics and focal length, but the final design will have a wooden tube, probably octagonal or multi-segmented. Inlay? Decoration? Reinforcement to avoid wood movement? Time will tell.

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