The Nitty-Gritty of Telescopes: Lenses, Filters, Doublers, and Prisms
Focal Length & Magnification
How far above wood do you have to hold a magnifying lens in the sunlight to make the smallest point possible so that you can burn something? That distance is specific to each lens, so whatever it may be, it is the focal length (FL) of that particular lens.
Magnification, on the other hand, is a mathematical function, and its units are delineated by the letter x, which is read as “power” or “times" when spoken aloud. Before Galileo Galilei, telescopes had a magnification of 3x or less and were used for sea navigation.
To calculate magnification power, you divide the focal length of the objective lens (the one closest to the object being viewed) by the FL of the receiving lens or eyepiece. If the primary lens has an FL of 900 units, and the eyepiece has an FL of 135 units, it provides a magnification of ~6.6x. This is similar to what Galileo achieved with his extraordinary astronomical telescope over 400 years ago.
If the two focal lengths were 300 units and 15 units, respectively, the magnification would be 20x. The focal length of any telescope is generally fixed, based on the design used. However, by changing the eyepiece’s FL, you can drastically alter the magnification. If the eyepiece in this example was substituted with a lens having an FL of 2.5 units, the magnification would increase to 120x.
"Units" is a substitute for millimeters, inches, or any unit of measure. In the scientific community, we use the international metric references, because they are easier to work with, and conversions are a matter of moving a decimal point rather than complex calculations.
NASA made metric-use obligatory for all participants after the Mars Climate Orbiter destruction and crash on the Martian surface in 1999. Lockheed Martin insisted on using "feet" and "pounds," while every other contractor on the project was using metric measurements, and faulty conversion mistakes ended that costly $125 million mission in dramatic fashion… If needed, we’ll use millimeters here, since that is most common. One inch ≌ 25 mm, if that works better for you.
Filters come in quite a variety, though you’re unlikely to use them at first. They are for many specialized purposes. We use colored filters to limit certain wavelengths of light to improve contrast or make details easier to see. We use polarized filters to restrict light coming from one specific direction. Some filters help us eliminate the effects of too much light pollution from cities. There are even filters that help us remove the effects of chromatic aberrations from some lens combinations.
We have special neutral density filters that limit incoming light for observing bright objects. The Moon is a painfully bright object in a telescope, and its brilliance can ruin your night vision for many minutes so you can’t see dim objects. We even have solar filters for the Sun, since that could permanently destroy your vision if you were to look at the Sun unprotected.
As an alternative, we can use aperture restrictors for lunar observation, such as on this reflector type telescope. What ordinarily acts as a dustcover also possesses a small cap which can be removed and stored on a built-in cap holder. The smaller aperture effectively turns a 178 mm aperture into a 51 mm aperture, which means it collects ~12 times less light. The advantage here is that the image is less intense, but it is not colored or tinted by a filter. It produces a true-color image for photographic purposes.
Barlow lenses are popularly called doublers because the most common sort increases magnification by two times (2x); however, Barlow lenses come in 3x or even adjustable models. They use 2, 3, or 4 lenses to avoid chromatic aberrations, but their real purpose is to decrease the focal length of the eyepiece.
In our earlier example of the 300 mm FL for the objective lens and a 2.5 mm FL for the eyepiece, the magnification was 120x, however by adding a 2x Barlow lens, the eyepiece’s FL would become 1.25 mm resulting in a magnification of 240x. Barlows are inexpensive, often <$10, so they are an excellent investment, effectively giving each eyepiece you own two different values.
The first time you look through a telescope, you may notice that the image is upside down. Is it broken? Nope. Every lens turns what it sees upside down. If you look at a tree, the image of that tree is projected inside on the back of your eye, but it is projected upside down. It is your intelligent brain that turns it right side up.
The thing to remember is that if you looked at a tree and it was upside down, you would instantly know that was wrong. Roots down—leaves up—everyone knows that. If you were to look at Mars or Saturn, you would have no idea that it was the wrong way around because you never see it in any other way—and is space there is no up or down, so it makes no difference to astronomers, and it shouldn't bother you either.
If the Space Age of the 1960s had lived up to all its hype, the plans were that we would have had a research station on the Moon by 1980; a town by 1990, and a full-fledged city by 2000... Let's imagine that you’re on the Moon now, looking back at Earth.
The left image is what you would see with your eyes. The center image is what a telescope would see (unmagnified). If you added a prism called a Star Diagonal, it would look like the third image. It would be upright, but it would still be swapped from left-to-right.
There is one more prism called an Erect Image Prism. Not only does it orient the image top-to-bottom as you would expect to see it, but it also swaps it left-to-right, so it gives you a properly oriented true image. For astronomy, it is virtually useless, and very few people use them, however, if you use your scope for terrestrial photography, say capturing images of birds, then it can be useful.
Unfortunately, an Erect Image Prism only works on a refractor or a catadioptric telescope (aka Schmidt-Cassegrain telescope), because the light path is straight. It is not useful with a reflector telescope because the image is sent out the side of the tube to the eyepiece, and is rotated in one direction instead of both so the image will always be wrong in one direction.
Reflectors are great for astronomical observations, collecting lots of light, performing exceptionally well, and being modest in price. They are not very useful as terrestrial telescopes, but that was never their purpose.