# How do focal length, angular magnification and field of view relate?

The larger the focal length the larger the angular magnification The smaller the focal length the larger the field of view.

I don't understand why this applies. I'm talking specifically about telescopes.

Wouldn't a greater angular magnification imply a greater field of view too?

• You will get a lot more useful information in photography.SE . Often people are confused because, strictly speaking, a telescope does not form a real image, whereas a camera does. Apr 20 '20 at 18:58

For the relation between magnification and field of view, imaging enlarging pictures, but you can only print out pictures on one size of paper. If you don't have a lot of magnification, you can draw out the entire face of a person in the picture, so you have a big field of view. If you magnify the same picture a lot, you might only get to see the nose or an ear in the picture, because everything else will be cut off the edges: you have a small field of view.

For the relation with the focal length, see the following schematics. You can find the rules on how to trace such schematics here.

In red are the light rays from an object at infinity that is aligned with the axis of the lense. In blue, there is an object that is also at infinity, but is at the edge of the field of view. If the focal distance is longer, then the object in blue and the object in red are close together in the sky, so the field of view is smaller, but the things you see in the focal plane appear to be bigger.

In short, top sketch: short focal length, big field of view, you can see all three objects. Bottom sketch: long focal length, small field of view, you can no longer see the green object

The field of view is the portion of the sky that you see in your eyepiece, measured in degrees. A human can typically have a field of view of 200° with two eyes. If you had eyes in the back of your head, your field of view would be 360°. The two objects in the top sketch are separated by a larger distance in the plane of sky than the two objects in the bottom sketch. In other terms, the apparent angle between the two objects is bigger in the top sketch than in the bottom sketch.

• Thank you! This helped massively!
– XXb8
Apr 21 '20 at 8:32
• Could you explain why they appear closer? Looking at the diagram it looks like they're separated by the same vertical distance
– XXb8
Apr 21 '20 at 9:08
• @XXb8 In both diagrams, the images of the objects are separated by the same vertical distance in the focal plane (where you put your eye). But the objects themselves are separated by a smaller distance in the bottom image. Apr 21 '20 at 9:11
• Yes this makes perfect sense now! Many thanks!
– XXb8
Apr 21 '20 at 9:32
• @XXb8 Top sketch: short focal length, big field of view, you can see all three objects. Bottom sketch: long focal length, small field of view, you can no longer see the green object. Apr 21 '20 at 9:32

Magnification and Field of View are directly opposite. A low magnification will give a large field of view, and a high magnification will give a small field of view. (Field of view indicates how "wide" is the portion of sky that is viewable in the eyepiece.)

Think of looking at the Moon with low power. Let's say the Moon fills 1/4 of the view, meaning that you could get 4 Moons lined-up side by side across the view. When you increase the magnification, the Moon looks bigger, so it fills more of the field of view. And therefore, you can get fewer Moons lined-up side by side. If you double the magnification, the Moon fills 1/2 of the view, meaning you can now only get 2 Moons side-by-side in the view.

Note that the above example is unusual for a telescope, depending on the design of course. Most astronomical telescopes used by amateurs will show an area of sky slightly larger than the Moon when using "low" power. Being able to fit 4 Moons is a bit of an exaggeration, for easy of explanation.

• I don't understand how a low magnification will give a large field of view, and a high magnification will give a small field of view. Is there a diagram to show this?
– XXb8
Apr 20 '20 at 14:36

Perhaps your confusion is that we refer to "Field of View" as the object (distant stuff) angular field that can be seen by the human eye without moving the eye. This is what 'usernumber' s answer is getting at.

Because the eye itself has a limited image diameter (size of retina combined with focal length of the eye), we map that field of view with whatever angular magnification the telescope creates. So it's not the "available" output FOV but rather the input FOV that can be captured by your eyeball.

It is daytime outside, you deep are in a long straight tunnel without lights. You notice that you can only see a small part of what is outside the tunnel and as you get closer to the exit you can see more and more of what is outside.

When you are deep in the tunnel it is darker because only the light rays that coming straight into the tunnel are going to reach you. If you were collecting photons you would be collecting them slowly.

When you moved closer to the exit it got brighter because rays of light from more places could reach you ; your photon collection efforts would be fast.

for a given primary (diameter of tunnel) long f means less "outside" area from which to gather photons (slow) short f means more "outside" area from which to gather photons (fast)

This analogy stops being intuitive when we switch to magnification because when you are deep in the tunnel things outside appear smaller because you are further away. But telescopes are different than our eyes in this respect and every view you get of outside no matter how close or far remains your whole field view which can then be magnified .