How a Telescope Works
The simple way I used to understand How a Telescope Works, was leaving
theories and formulas aside for a minute and just think about the obvious.
The text, drawings and explanations in this webpage is oriented to the newbie in telescopes, it explains in a
simple way how lenses work and how they are used to enlarge and magnify images inside a telescope.
I don't use complex formulas and theories, don't expect to find complex explanations, and some
assumptions here may be a little be off the course, but the easy compreension is certain.
Simple as it is, several people found here the understanding how a telescope works.
After 56 years and a cancer, I decided to learn telescopes and astronomy, so in January 2011 I bought few
scopes and started to dedicate many hours to understand everything related and found that I knew very little
or nothing about optics. The curiosity and necessity to understand lead me to found several answers, mostly
at the foruns "CloudyNights.Com", where I found several helping and courteous people.
I conducted some optical experiments and simulations myself, read a lot, and then, read a lot more.
English is my third language, I made the best effort to avoid many mistakes in the text below.
Wagner Lip - wagner at ustr dot net - April 2011
A proud user of Google
When you are close to a big tree, your eyes can not see the whole at once, you even need to turn your head up to see the tall branches. The angle of the whole image is so large vertically that your eyes can not see it at once. Your eyes have a limited angle of seeing. I measured mine and I can see a maximum of 116 degrees vertically.
Figure 1
If I distant myself 10 to 15 steps from the tree, to allow me to see the whole tree, the angle of the image will be less than 116 degrees, Figure 2. Now the tree image angle is smaller than at figure 1, and the tree image fits entirely inside my retina.
Figure 2
If I walk away 80 steps or more from the tree, I will see lots of things around, houses, cars, street, and in middle of everything a small tree, with a very small angle of image, figure 3, probably the tree image will be in an angle around 11 degrees, 10 times smaller than before.
Figure 3
So, to see big, the image needs to enter your eyes with large angle. If it enters with small angle, almost parallel, you will see a very small image. This is due the eye lenses. Parallel ray creates a single dot in the retina, no matter where it enters the eye. Different angle of incidence into the eye, but parallel, will create a tiny spot in a different place of the retina. When you look at the sky at night, naked eye, and see several bright stars, each star is sending to you parallel rays, but each one of those beams of light enter you eye in a different angle, producing a single dot of light in different places of your retina.
For example, if you put your finger right in front of your eye, really close, almost touching your eye, your finger will be out of focus, but you will see it bigger than a car, truck, house, even that tree. Why? it is not only because it is close to your eye, but its image is entering your eye in a steep angle. If you didn't know better, you will think it was a very large thing. Moving your finger from the eye, the image angle will becoming smaller and smaller, and also the image of your finger. So, what defines big or small into your eye, is the angle the rays of light of such image enter your eye, and not exactly the real size of the object.
Small Angle = Small Object Image
Large Angle = Large Object Image
What the telescope lenses do, is just get a narrow angle (almost parallel) image (the far away tree), expand and bend the light rays in a way to enter your eyes in a large angle (like a parrot beak), the same angle you see when closer to the tree of your finger over your eye. In other words, what you always heard is correct, the telescope "brings" things closer.
Figure 4
Now, how the telescope does that?
A Convex lens has the ability to bend light rays inwards, in a way to make parallel beams to concentrate in a single point, called focal point. As much angled (fat in the center) the lens has, faster (more angle) the rays will bend, and the focal point will be shorter.
I will not explain in details how a lens bend light, but think when you are driving your car in the rain and the right tires enter a foot of water at the right side of the street close to the curb, your car will push to that side. Since the water drags the tires and acts as a breaking system, while the left tires are running free, the car will push and turn to the right. The same for the lenses, the first side of the beam of light to hit the lens will bend to that side, since the lens is denser than air, and it acts as the water in the tires. In real, when a beam of light moves from air to denser matter, like glass or water, its speed slows down, the light ray travels slower. The other side of the beam, still travelling fast, will push the beam to the slower side, this is the first bend (entering the lens).
The same happens for beams exiting lenses, the first side of the beam exiting the lens, speeds up and will push (bend) the beam to the slower side. This is the second bend, exiting the lens.
Figure 5
Now, a biconvex lens has the same focal point for both sides. Figure 6 shows that no matter from what side the parallel rays enter the lens, the ray beams will concentrate at the other side focal length and focal point.
Then, if you have a biconvex lens with 10" of focal length, and you install a lamp 20" from the lens and a paper card 20" from the other side of the lens (both at double focal length distance), you will see the lamp filament or the whole lamp projected in the paper, in the same exact size of the real lamp. This happens because at the double distance of focal length, a point of light will be bend by the lens the same way at the entry and at the exit, not changing anything. So you can say that a simple biconvex lens will not magnify or reduce the image at double the focal length from one side to another, just transport it, with magnification x1.
Figure 6
The lamp was not generating parallel rays, it spreads light everywhere, but what hit the lens is a cone of light. If the lens is locate at exactly twice the distance of focal length from the lamp, the lens generates another cone of light at the other side. It will be a single dot of light at that focal point and will open again another cone that will project forever in that angle.
Note that the bi-convex lens bend the light twice, at entry and again at exit, and in the case above, the rays inside the lens are parallel due the first bent.
Now, if we move the lens to the left, at exactly the focal length distance from the lamp, the exit of the lens will not be a cone, but parallel rays that will tend to move like that to the possible infinite, see Figure 7 below. But if you move the lens to the right, increasing the distance from the lens to the lamp, the parallel rays at the right will start to concentrate, more and more, until they concentrate to a single point, at twice the focal length (20"), exactly as Figure 6 above.
Figure 7
See Figure 8 below, a tinny bright star brings you parallel rays of light at the left. The bi-convex lens will double bend the star beam of rays in the same way, but as they are parallel already at the entry of the lens, inside the lens they will bend some, and will bend again at the exit, concentrating to a Focal Point exactly at the Focal Length.
Do not confuse Focal Length with Focal Point.
Focal Point is where the beam of rays concentrate to a point, no matter the angle of the beam of rasys entering the lens at the left side. Were ever a beam of rays focused in a point, that is the Focal Point. Now, Focal Length of a lens, is the distance from the center or the lens to a Focal Point, when the entering beam of rays is parallel, as the Figure 8 below. So, below you can see at the right edge, vertical blue line, the Focal Point "and" Focal Length at the same place.
Figure 8
Ok, now you know how lens can bend light. A lens with more angle, bend light strongly. Remember the water in the tire, as longer (more angle) the water offers resistance to the right tires, more the car will turn to the right.
Lets use the example of a Refractor Telescope, a telescope that uses a minimum of two lenses. The big one at the front is called "Objective", the smaller is the "Eyepiece", closer to the eye.
The main function of a telescope is magnify the brightness and size of an image. To do that, the objective lens must have a longer focal point than the eyepiece. As a matter of fact, the magnification of the telescope is exactly the result of the division of the focal point of the objective by the focal point of the eyepiece. So, to change magnification of a telescope, we use to change the eyepiece for another with longer or shorter focal point. Shorter focal point at the eyepiece increases the magnification of the telescope.
But the question is: HOW IT DOES THAT?
The objective lens with longer focal point, will not bend the light too much, just a little, but enough to bend the light from the far tree more than the original incoming rays. Lets say the tree is at 200 meters away, its rays are almost parallel, less than 10 degrees. The telescope objective is responsible to bend the light in a controllable way and keep the focal point inside the telescope, lets say, to one meter focus, inside the telescope tube. But still, the top of the tree is entering the objective in a different angle than the trunk, the image enters the telescope with a small angle difference, but it exist. The objective will bend the light a little bit, making the top and trunk of the tree crossing each other a little bit before the eyepiece, and entering the eyepiece after they cross each other and entering the eye with a large angle than the angle that came from the tree. I will explain it better later in this text.
Now I will show a lot of figures of lenses and ray traces. It will be much easier to see what happens. In all the following drawings, the ray light comes from the left. The right blue vertical bar is to be considered your eye retina. The blue lens 4 lines to the left is your eye lenses. All the drawings are just representation, they are not in correct proportion, and not represent exactly the lenses shape. The way they are, is just to help demonstrate the ray tracing.
First let me show you how a small bright star light, parallel rays, enter your naked eye. They travel very parallel until they hit your eye lenses. The lenses bend the light and concentrate such light in a single point in the retina. Your eye automatic focus system will adjust your eye muscles to see the smallest point possible. If you suffer from miopy, your eye will not be able to make such adjustment, then you will need glasses, external lenses to compensate and help the eye lenses to concentrate the star light into a focused tinny point of light in the retina.
Figure 9
Now, suppose the rays from the left side comes from that far tree, 200 meters or more away. The tree spreads light everywhere, to all angles, but the ones that could reach your eye are represented below. Note how the rays from the tree are closing as they are traveling to your eye. At the tree, the top and trunk rays, they must enter your eye, so they form a cone reducing the size, forming a cone of light. In real the light is spread all over, but the useful for your eye, is the cone. Note a very small red triangle at the retina, those are the rays from the tree image forming on the retina, a small tree indeed.
Figure 10
Looking at a Star using a strong lens (Eyepiece)
Now, what happens when you look at a star through a short focus lens, for example, a telescope eyepiece without the telescope? Remember that magnification is the result of the division of the objective focal point by the eyepiece focal point? Well, without objective, is the same as a piece of window flass, an objective with infinite focal point, so the magnification is also infinite and without focus. If you look at a star with parallel rays, the magnification is infinite. You will see a blur light.
Figure 11
Looking at a Star using a long focus lens (Objective)
Then you take just a telescope objective, a wide diameter convex lens with around 100mm in diameter, with a long focus length of almost 1000mm, and look through this lens to a tinny bright star, parallel rays coming from the star. The lens must be around 1 meter from your eye. Based on the drawing below, what can you see?
Figure 12
Considering the Objective Convex Lens has a focal length of 1000m (left cone of light) and suppose that your eye can make a focal length of 20mm (right cone of light), and that both focus points are in the same place, the objective lens will be at 1020mm from your eye, the parallel rays from the star will enter the objective lens, will be bend to the focal point, will expand and enter your eye, it will bend the rays back to parallel, they will hit your retina in a disk of difused light. You will see the tinny bright star as a larger disk of difused light, out of focus.
Remember from the start of this webpage, large tree - large angle entering your eye, small tree - small angle entering your eye? Well, again, the bigger the angle the image of an object enter your eye, the bigger you see the object. A small far away object image enter your eye with a small angle. To magnify it, we need to increase the angle of such object image. Simple as that. Lenses are very good to bend light, so a set of lenses arranged in some way, could bend light in such way that we change the trajectory of the far object image and make it enter your eye in a large angle, so we will be tricking your eye to actually "see" this small object image as a big one. That's the magic of magnification.
First of all, let me remember you what happens when a parallel beam of light rays enter your eye, your eye lens refract the rays to a single point into the retina, right? Exactly as the drawing below:
Figure 13
All the telescope lenses together
Ok, now, look the drawing below. A large objective lens, 100mm in diameter (Aperture), receives a lot of parallel rays from the star, refract all the rays into the focal point (1000mm behind it), the eyepiece lens (30mm focal length) in front of your eye bend the expanding cone of rays to parallel, but now all the rays into a smaller diameter of beam, lets say 5mm, and that parallel beam enter your eye. The eye lens will refract again to a single point into the retina.
So, parallel from the star into a single point into the retina, exactly as the drawing above. The big difference is that in the drawing above, what enters your eye is a 5mm diameter beam of parallel rays directly from the star. That is not much rays of light. In the drawing below, a beam of 100mm of parallel rays will be compressed to 5mm beam of parallel rays and enter your eye. Did you understand that? The objective and the eyepiece lenses, compressed much more light into your eye, lots of rays from 100mm diameter to 5mm diameter. You see the star brighter, now you can see stars that were much dimmer before, some you could not even see at naked eye, now they are visible.
Lets do some single math, area of a circle is Square of Half the Diameter times PI (3.14), then, 5mm beam of rays represents around 19 square milimeters of area, but the 100mm diameter objective lens has around 78 hundred square milimeters of area. It means the objective lens can capture 413 more rays than your naked eye. You now can see stars 413 times brighter. But that is just "brighter", not bigger, since the tinny far star with parallel rays, will still creating a single point of light into your retina, there is a a very tinny magnification or in some cases, none.
Figure 14
Remember, to see big we need to increase the angle the image enters your eye. In the image above, the rays entering your eye still parallel, as they came from the star. The both lenses did not increase the rays angle, they just compressed more rays, more light. The reason for not being able to magnify a focused distant tinny bright star, is that the star rays did not came in an angle, they came parallel. Well, if you move the Eyepiece lens back and forth, you will in fact increase the dot into your retina, you will see a blurred disk of light, it IS in fact the star magnified, but out of focus and it worths nothing. Good and usefull magnification should mantain focus of the object image at the retina.
To do that, the object sending beam of rays should be big and not at the infinite, enough to send its rays with a tinny bitty angle, so they could be bent to enter the eye in a larger angle, so we could keep focus and provide magnification.
Well, confused? Imagine a car very close starts to run away from you. At first you even need to move your head to see both break lights and the whole car's body from behind. Few seconds later, it will be 50 meters or more away, you are still able to see both break lights, but now you don't need to move your head, since the whole car's body image fit inside your retina. After he moves 2 or 3 blocks away, you can't really tell what kind of car is there, and you can't see exactly the break lights, but you can see a minuscule car there, there is some size in the image, and with a good instrument you will be able to measure the tinny size of the car, and with it, the different angles from both the break lights. For sure there is an angle and they hit your retina in a tinny angle. This angle is what allows the telescope to magnify the car's image. Now, if the car is in the moon, it is so far away, the angle is so tinny bitty small that the telescope can not resolve the image, can not magnify. If the car in the moon produces a very very strong light, you probably will be able to see such tinny dot of light, but will not be able to magnify, to do it, you will need a tremendously large telescope, with a primary lens with many meters in diameter.
Figure 15
Figure 15 shows the distant object at the left, sending its rays with a little angle, like the car at 10 blocks away, it means it has some measurable size (at distance). Now think about our Sun, it is very far away, but you can see its disk in the sky, you can even measure it. Stretch your arm, you can cover the Sun's disk with your thumb. It is around 1/2 a degree, and if using a ruller, it covers around 25mm at your arm's length. The same for the Moon, same size, but closer, around 300 thousand kilometers.
The Sun is very far away, but it is very big, so you can see its disk in the sky, it can be magnified easily by any small lens, the same for the Moon. This is possible since the light beams from Sun's edges reach the Objective lens of a telescope with half degree angle. Compare figure 14 and 15 above, see the tinny point where the red rays concentrate around the center of the figures. Figure 14 shows this point is closer to the eyepiece lens (to the right), since the incoming rays are parallel. Figure 15 shows this point more at the center. This change of position is caused by the tinny angled incoming rays, from "top" and "bottom" of the object, the edging rays. Figure 15 shows the same lens now concentrating the rays in a shorter position. After that concentration point, the expanding cone of rays will reach the eyepiece with a wide diameter than the first drawing. The object top edge is now almost at the bottom edge of the eyepiece, and will be bent more drastically to the eye. Figure 15 shows how the rays are more angled between the eyepiece and the eye ("Rays with large angle"). Figure 14 shows these same rays parallel.
This is the magic of magnification. MagicNification? 
This steep angle, when projected backwards (in blue line in Figure 15) is almost the same as when looking close to a big tree, remember? So, now look at the projected image at the retina of Figure 15, the projected focused image takes almost 4 squares of the drawing grid screen, and the image is right oriented, top object image to top of retina. But remember, our brain will see that magnified focused image upside down.
So far so good, it was magnified, but how much?
Magnification is basically the result of the Objective Focal Length divided by the Eyepiece Focal Length. But Why ?
Because the capacity of the both lens together to bend the light. That is a mechanical angle setup. If both the lenses, objective and eyepiece has the same focal length, they will bend the light beam exactly the same, one way and then again. The angle the beam enters the eye, delivered by the eyepiece, will be exactly the same angle the beam enters the Objective, so magnification is null.
In the Figure 15 above, the objective has 1000mm of focal length, the eyepiece has 30mm of focal length, the magnification is 1000/30 = 33. It means that the object image rays angle entering the eye is much bigger than the angle they entered the objective lens ("Rays with little angle" vs "Rays with large angle"), that is the tricky thing. When you see and understand the different angles, and that as big is the result of the division "Objective focal length by Eyepiece focal length", more bent will be the light entering the eye, you will understand the telescope magnification clearly. If you don't, read again until you grasp the idea. This is not a believing thing, this is just logic.
So, as a gross measurement, note the 3.7 squares of the grid the projected image ocupies at the retina, and consider it magnification = 33.
Now, I changed Objective lens at the Figure 16 below, now it has a focal length of 80mm, still 100mm in diameter (aperture). Note the objective is not so far left anylonger, I needed to move it a bit to the right in order to keep the projected image in focus at the retina. Now the magnification is 800/30 = 26.6x, and see how the projected image at the retina is smaller than the one at Figure 15 above, now it occupies around 2.8 squares of the grid. Also see the angle of the rays between the eyepiece and the eye lens, they are not to steep as the one at Figure 15. So, less magnification, less steep the angle of the image entering the eye. Remember, the tree image fiting the whole eye?
Figure 16
The next drawing I used an objective lens with shorter focal length of 60mm, still 100mm of aperture. Now to project a focused image at the retina, the objective lens must be closer to the eyepiece, and the magnification is 600/30 = 20x. Note the smaller angle of the rays between the eyepiece and eye lens, but still, this angle is larger than the angle of the rays entering the objective at the left. Note also the projected image at the retina occupies only 2.2 squares of the grid.
Figure 17
See Figure 18 below, a zoomed area of this rays from Figure 15, 16 and 17. See the green lines, larger angle with 33x, smaller angle with 20x.
Figure 18
Well, in the above drawing examples, it was easier for me to replace the objective, since the eyepiece was so close to the eye that it would be complicated to draw and for you to see. In real life, you don't change the objective lens, it is big and expensive, so you change the eyepiece that is small and easy to store several in a box. So, changing eyepiece with different focal length, you obtain different magnifications. The photo below is from a Sky Watcher Pro 120ED APO Refractor OTA. You can see the major parts of the telescope.
The Objective lens is installed inside and at the front of the tube (OTA). Over the front there is a cover, a shield, to block some stray light and dew at night, a major problem for observing when dew form over the objective lens. Also, you can see the "focuser", it moves the whole back of the telescope (diagonal and eyepieces) back and forth to locate the exact position and focuse the image at the retina. The focuser tube goes inside the telescope tube and is moved by means of sliding track and gears. The "diagonal" is basically a flat mirror that bend light 90 degrees to the above, to enter the "eyepiece". It is much easier to watch the sky looking into the eyepiece in that position, so you bend your head down or at most, forward, when watching the sky at the horizon or at the zenith.
The "View Finder" or "Finder Scope" is a small telescope, normaly magnifying only 5 to 12x, to help to position the telescope where it is mounted, in some position in the sky. Due the large magnification of the main telescope, sometimes is very difficult to pinpoint some exact position in the sky, so we use the small one to give a "ballpark" position, then fine position with the main one.
The "eyepiece" is removable from the diagonal, you install different eyepieces for different magnifications. In real, the market is full of hundreds of different eyepieces, each manufacturer working to produce the best eyepiece ever. Some deliver more clearer image, others wide image, etc. In some cases an eyepiece may cost more than the whole telescope. It is not rare to find eyepieces that cost above $600, while the basic eyepieces can be found by a low cost of $30 to $50. Most astronomers say the eyepiece is the most important part of the telescope.
Very old telescopes used eyepieces produced especially for them, a caos in the market. After some confusion times, some standardization was done, and then telescopes started to use eyepieces with diameter of 0.968". Later a larger eyepiece was introduced in the market, and 1.25" came as standar, until today. Eyepieces of 2" are in the market, more expensive, they give you more light and more field of view, but they provide more benefits when used in very large mirror telescopes, with 10" and larger apperture mirrors (objectives). The telescope below sell by $1599 at Telescope.Com and other places.
Eyepieces are identified by their focal length. Below you can see some eyepieces, Baader Planetarium Hyperion, identified as 13mm, 17mm, 21mm, 24mm, 3.5mm, 5mm, 8mm and 10mm. They are specially produced in a way to fit both, the 1.25" and 2" diagonals. The magnification each one produces depends on the telescope objective focal length. Remember, dividing one by another gives you the real magnification. If the Objective is 1000mm, then a 21mm eyepiece will produce 47.61x magnification. These particular eyepieces sell by aproximately $120.00 each at Telescope.Com and other places.
Thanks for visiting. Wagner Lip, April 5, 2011