4. What Does a Telescope Do?

This isn’t such a trivial question as you might think! A substantial proportion of people don’t actually know the correct answer. That fact, combined with the willingness of some unscrupulous manufacturers to exploit it, results in a lot of money being wasted on telescopes which are little more than junk, and lots of children’s interest in astronomy being killed off almost before it has begun.

4.1. “Department store telescopes”

Every Christmas, thousands of well-meaning but naive parents buy a small telescope for a child who has developed an interest in astronomy. Many of them, thankfully, have the good sense to ask an amateur astronomer, such as the secretary of their local astronomical society, for advice on what kind to buy. The advice which we usually give them is: “Don’t! At least, don’t buy the kind of cheap telescope which is sold in department stores. Buy them a decent pair of binoculars to start with – then progress to a bit more expensive telescope when the child is a bit older, if their interest becomes serious.”
Those who don’t think to ask an astronomer for advice usually end up buying the very thing which the latter would have advised them not to!
The aforementioned kind of cheap telescopes, which are often sold in department stores, and marketed for children, are usually small refractors, with apertures ( the diameter of the main lens ) of 50 or 60 mm. The cheaper ones are little more than toys; the optics are usually of poor quality, and the tripods often so flimsy that you can’t hold the telescope steady anyway. With such things, you can usually manage a half-decent view of the Moon, and not much else!
There are in fact many 60-mm refractors which are of far better quality, and correspondingly more expensive; these are usually sold by reputable camera shops, rather than department stores. In the world of amateur astronomy, the phrase “department store telescope” is used as a generic derogatory term – derogatory, that is, towards those who make and sell such things, rather than those who buy them.
The reason for the above advice is quite simple – because any decent quality pair of binoculars, of 50 mm aperture or bigger, is likely to give better quality images than a cheap department store telescope! They also have the advantage that if the child loses interest in astronomy, the binoculars can also be used for terrestrial pursuits, such as bird or wildlife watching – which many telescopes can’t, as they produce an upside-down image!
By the way, if you buy a pair of binoculars for the purpose of astronomy, don’t assume that higher magnification is better – it most certainly isn’t! The reason is very simple – the higher the magnification, the more difficult it is to hold the binoculars steady! So 7x50 binoculars ( 7x magnification and 50 mm aperture ) are better than 10x50s, and 16x50s should definitely be avoided.
Most telescopes which are really worth buying cost more than the average parent is willing to spend for a young child; as a general rule, any telescope which costs less than a couple of hundred pounds or dollars isn’t worth bothering with.

4.2. Magnification and resolution

So what does a telescope actually do? What is its purpose? If you asked that question to a lot of laypeople, with no knowledge of astronomy, the majority would probably say “to magnify things”, or “to make things appear closer”. And they would be wrong. While every telescope does indeed magnify, that is not its primary purpose – but it’s that misconception which is exploited by some unscrupulous manufacturers of department store telescopes.
Many parents, who want to buy a telescope for a child, but know nothing about astronomy themselves, naively assume that the more it magnifies, the better. The aforementioned manufacturers cash in on that belief, by advertising their telescopes as providing ridiculously high levels of magnification. It’s commonplace to see 60-mm refractors with something like “Magnifies up to 400x!” emblazoned on the box. While such claims are not actually false – an eyepiece is provided which does indeed produce that magnification – they are definitely misleading. Using a small telescope with such magnification is in fact useless – or even worse then useless. For any given size of telescope, there is a maximum useful magnification, which for a 60-mm refractor is about 140x; using any higher magnification makes no difference at all to the amount of detail you can see, for reasons which I’ll explain shortly.
The real purpose of a telescope is twofold – to collect light and to resolve detail. The latter is not the same thing as magnifying! Both of these depend on its aperture, i.e. the diameter of its primary lens ( or mirror, if it’s a reflecting telescope ), which astronomers call the objective.
First, collecting light. It’s obvious that the bigger the objective lens ( or mirror ), the more light it can collect and focus; the amount of light collected is proportional to the area of the objective, which in turn is proportional to the square of its diameter. ( The area of a circle of radius r is p r2. ) And the more light a telescope collects, the fainter the stars or other objects you can see – it’s that simple! If you look at a cluster of stars, you can see more stars with a bigger telescope, as it reveals fainter ones. And any given telescope enables you to see certain nebulae and galaxies which are beyond the capability of a smaller one. That’s an over-simplification, as there are other factors which affect what you can and can’t see – but the simple principle is that a bigger telescope goes fainter.
Now for the matter of resolving detail. Every telescope has a certain angular resolution, which is inversely proportional to its aperture; the bigger the aperture, the smaller the angular resolution. This is a measure of the level of detail which your eyes can discern in the image; the bigger the aperture, the finer the detail you can see. It actually means the closest angular separation at which points of detail can be distinguished, without blurring together. This limit is imposed by the fundamental properties of light; it simply isn’t possible to see finer detail by using a higher magnification. There’s a mathematical formula to calculate it, which I won’t bore you with here.
Explaining this in detail is beyond the scope of this essay, but I’ll try to do so very briefly. Imagine looking at a double star – two stars very close together separated by a few seconds of arc. For any practical purpose, stars can be regarded as point sources of light; their actual angular sizes are so miniscule that we can regard them as zero. But due to a fundamental behaviour of light called diffraction, a point source never actually appears as a point, but as a tiny disc; the bigger the telescope aperture, the smaller is this disc. So if two stars are so close together that their two discs overlap, then you can’t distinguish them; they blur together into a single elongated blob.
When looking at anything which isn’t a point source, the level of detail which can be discerned is limited by similar effects.
For example, the theoretical angular resolution of a 60-mm telescope is about two seconds of arc, and that of a 20-cm telescope – a typical size used by serious amateur astronomers – is about 0.6 second of arc. In reality, however, it’s rarely actually possible to achieve a telescope’s theoretical resolution, as it’s limited by effects of the atmosphere.
To visualise the concept of angular resolution, you can do a simple experiment. Look across a car park at a car some distance away, and see whether you can read its number plate. If it’s further away than about 120 feet, you almost certainly can’t; the number plate will be a blur. Now walk slowly towards the car; at some particular distance, you will find that you can just about make out the letters and numbers, then as you get a bit closer still, you can read it clearly. In my country, reading a number plate is used as a simple test of eyesight for being allowed to drive; you must be able to read a standard size number plate at a distance of 75 feet. Driving instructors must be able to read one at 90 feet. With my distance glasses, I can clearly read a number plate at up to about 100 feet; beyond about 120 feet, I can’t read it at all.
Obviously, the further an object is from your eye, the smaller it appears. That is, the smaller is its angular size – the angle which the object subtends at your eye is proportional to its actual size, and inversely proportional to its distance away. The angular resolution of the average person’s eyes – with your glasses, if you wear them – is about one minute of arc, i.e. one sixtieth of a degree.
Note that angular resolution refers not to the size of objects which you can see, but to the separation of detail. Go back to my number plate example. If you look at a car from a distance of, say, 200 feet, you can still see the number plate itself, but you can’t make out the letters on it. At 120 feet, you can probably distinguish the letters as separate black blobs, though you still can’t make out what letters they are.
I’ve already mentioned double stars. For any given double star, a certain aperture of telescope is required to resolve it into two stars, depending on their separation; with the naked eye, or with a smaller telescope, they blur together and look like a single star.
As another obvious example; when looking at the Moon, a bigger aperture enables you to discern finer details, such as smaller craters or mountain peaks.
Now we come to the matter of magnification. This is determined not by the aperture of the objective lens or mirror, but by its focal length. 60-mm refractors typically have a focal length of around 700 mm. ( Astronomers often refer to the focal ratio of a telescope, denoted by f/ and a number. This means the same as the “f stop” numbers on a camera; it’s equal to the focal length divided by the aperture. Thus a “60-mm f/12 refractor” has a focal length of 60 x 12 = 720 mm. The focal ratio is very important to those who use their telescopes for photography, but not for visual observing. )
The primary lens or mirror of a telescope focuses light to form an image at the focal plane, which is the focal length away. This image is then magnified by the eyepiece - the small lens which you look through. The magnification is equal to the focal length of the objective divided by the focal length of the eyepiece. So if your refractor has a focal length of 720 mm, then using an eyepiece with a focal length of 24 mm gives a magnification of 720 / 24 = 30x, while one with a focal length of 12 mm gives a magnification of 720 / 12 = 60x. Small telescopes usually have two or three eyepieces supplied, with different focal lengths, so you have a choice of magnifications.
So finally, we come to the reason why you can’t just magnify indefinitely. By using eyepieces of shorter focal lengths, you could indeed achieve any magnification you like – but doing so is pointless, for a reason which I hope will now become clear. The limiting angular resolution, for a telescope of any given aperture, is dictated by the laws of physics; you can’t see any finer detail, no matter how much you magnify the image. Using more than a certain magnification actually degrades the quality of your image, as you’re simply magnifying the blurring; it also has the detrimental effect of making the image fainter!
For any telescope, the maximum useful magnification is generally said to be about 60x per inch of aperture. Thus for a 60-mm, or 2.4 inch, refractor, it’s 60 x 2.4 = 144x.
So now we see why advertising such telescopes as “magnifying up to 400x” is just an unscrupulous marketing con!

4.3. A word of warning – IMPORTANT!

At this point, I’ll give the rather obvious but mandatory warning, which comes in any article about telescopes for beginners:
NEVER look at the Sun through a telescope or binoculars!

But since I’ve been talking specifically about department store telescopes, there’s also another warning which I need to give, especially to anyone buying one for a child. Many of these telescopes include among their accessories a so-called “solar filter”, which supposedly enables you to look at the Sun safely. It does not!!!
These filters are made from dark glass, similar to welder’s glass ( which of course serves a similar purpose ) and are made to fit over the eyepiece, or to screw into its barrel. They are not safe at all; they are dangerous, and in my opinion, making and selling them should be illegal!
Think about it. Read again what I said in the last paragraph – the filter fits over the eyepiece. That means that when looking at the Sun, all the light and heat which enters the telescope is focused onto the filter. If it’s used for any length of time, the filter will become very hot, and sooner or later, it will crack. And if a child is looking through it when it does... well, need I say more?
So if you do buy a cheap telescope for a child, and find that one of those filters is provided – bin the filter immediately! NEVER allow a child to use it!
The only safe solar filters are those which fit over the objective of the telescope, and therefore block almost all of the light and heat before it enters the telescope. Such things are available, but they generally cost more than a cheap telescope!
The safe and simple way to observe the Sun with a small telescope is to project its image onto a white card held behind the eyepiece. You will find that method described in just about any book or web site on beginners’ astronomy.

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