Why does a spyglass or binoculars zoom in?

[grindagrom]

Why does a spyglass or binoculars zoom in? How does it work? I know a little about optics. But here's what interests me: how does a beam of light entering the binocular lens bring the object closer? This beam of light has certain information inside, and this information is "decoded" by binoculars and enters the eye already decoded. It turns out that there is already all the information in this beam of light about the object or even more. Am I right?

 

[russ_watters]

I'm not sure that thinking of it as "information" that is "encoded/decoded" is useful. All lenses do is change the angle at which light hits your eye.

 

[Ibix]

As Russ says, changing the relative positions of the lenses changes the angles at which light enters your eye. So, for example, the angular diameter of the moon as seen from Earth is about half a degree. 8× binoculars would increase that to four degrees. That means you see less through the binocs than you would through an empty tube the same size, but what you do see is larger.

As an aside, there are limits to how much magnificaton is useful even with an ideal optical system. If you keep increasing the magnification there comes a point where you cannot see more detail - you just see blur, no matter how good your optics are. This is the "diffraction limit", and is a kind of limit on information transmitted through a hole of a certain diameter. Very few optical systems are diffraction limited - atmospheric distortion and design trade-offs usually degrade the image long before this becomes relevant.

 

[grindagrom]

I'm not sure that thinking of it as "information" that is "encoded/decoded" is useful. All lenses do is change the angle at which light hits your eye.

ok. Let’s take a light that came from a star. My eye just seeing a small dot in the sky but with binoculars or a telescope, I can see more information. But the beam of light that came from the star and hit the lens is very small. Where does information come from? Is it already there in the amount of light that comes? Let's take a more powerful telescope and it will give us even more information. But the light that hit the telescope cannot carry so much more information. So where does it come from?

 

[grindagrom]

As Russ says, changing the relative positions of the lenses changes the angles at which light enters your eye. So, for example, the angular diameter of the moon as seen from Earth is about half a degree. 8× binoculars would increase that to four degrees. That means you see less through the binocs than you would through an empty tube the same size, but what you do see is larger.

As an aside, there are limits to how much magnificaton is useful even with an ideal optical system. If you keep increasing the magnification there comes a point where you cannot see more detail - you just see blur, no matter how good your optics are. This is the "diffraction limit", and is a kind of limit on information transmitted through a hole of a certain diameter. Very few optical systems are diffraction limited - atmospheric distortion and design trade-offs usually degrade the image long before this becomes relevant.

Yes, I understand. but in the moon example, doesn't that mean I'll just see it bigger? How can I see it not only bigger but more detailed?

 

[grindagrom]

As Russ says, changing the relative positions of the lenses changes the angles at which light enters your eye. So, for example, the angular diameter of the moon as seen from Earth is about half a degree. 8× binoculars would increase that to four degrees. That means you see less through the binocs than you would through an empty tube the same size, but what you do see is larger.

As an aside, there are limits to how much magnificaton is useful even with an ideal optical system. If you keep increasing the magnification there comes a point where you cannot see more detail - you just see blur, no matter how good your optics are. This is the "diffraction limit", and is a kind of limit on information transmitted through a hole of a certain diameter. Very few optical systems are diffraction limited - atmospheric distortion and design trade-offs usually degrade the image long before this becomes relevant.

Does it mean that just changing the angles at which light enters my eye I can change the object size and detail?

 

[PeroK]

Does it mean that just changing the angles at which light enters my eye I can change the object size and detail?

If you look at a page in a book too far away, you cannot read the writing. That doesn't mean that the details are not reaching your eye, just that your eye and brain cannot resolve them. With a telescope, the details are magnified so that your eye an brain can process them.

 

[DrJohn]

I found this helpful
https://opticsmag.com/how-does-a-magnifying-glass-work/

The eye normally receives parallel beams of light from the target, those directly in front of the eye enter it and the eye's lens brings them to focus on the retina. Other rays not travelling directly at the the eye don't enter it.

As you can see in the diagram on that page referenced above, light that would not enter the eye - the parallel rays that end up hitting the skin above, below, to the left or the right - are bent round (refracted) by the lens and enter the eye, where they then get focused on the retina, producing a bigger image that you'd see without the lens.

Tracing back from the image on the retina to where the object appears to be (it's called a virual image) shows that the object would have to be bigger to form the same sized image on the retina. So it appears bigger.

I admit the optics wasn't my top topic in physics, as it required us to copy diagrams from the board accurately and our lecturer back then simply didn't give us enough time (deliberately, we all suspected, after he got replaced by a human being - he had a nervous breakdown from teaching us) so my notes where usually incomplete, which doesn't help anyone learn. Handouts with good diagrams back then were just not normally given to students. WWW means you can find them and study them to see what they mean.

So study the diagram and you will see what is happening to the light.

In the case of a star, the target star is occupying a tiny TINY area of your field of vision, so forms a tiny image in the eye. With a telescope or binoculars, many more light rays are refracted and give the bigger virual image that you see. The lens on the telescope or binoculars are much bigger than your eye's lens.

 

[russ_watters]

ok. Let’s take a light that came from a star. My eye just seeing a small dot in the sky but with binoculars or a telescope, I can see more information. But the beam of light that came from the star and hit the lens is very small. Where does information come from? Is it already there in the amount of light that comes? Let's take a more powerful telescope and it will give us even more information. But the light that hit the telescope cannot carry so much more information. So where does it come from?

A star is a bad example because it looks like a point of light either way. A planet, or the moon as in @Ibix's example, is better. The fact that you can see more detail when "zoomed in" is primarily due to the resolution of your eye. The "information" is spread across more rods and cones.

 

[Drakkith]

Does it mean that just changing the angles at which light enters my eye I can change the object size and detail?

Yes. That's exactly what a telescope or other similar optical system does.

Yes, I understand. but in the moon example, doesn't that mean I'll just see it bigger? How can I see it not only bigger but more detailed?

That's exactly what happens when you try to read a book from 50 feet away and then move to 2 feet away. The book's angular size becomes larger but so do the words on the page. The reason you can't read a book from 50 feet away is because the angular separation between letters (and between points within those letters) is too small. That is, everything is crammed together so close to each other that your eye can't tell the difference between one part of the book and another part close by. You can't 'resolve' the details. Zooming in or moving closer makes the book look bigger, moving the details apart, letting you resolve them.

 

[DrJohn]

Your eye have sensors that react to light. If the image only lands on a few sensors - rods and cones, they have a small amount of information to send to your brain. When you magnify the image, it lands on many more sensors, so the details are easier to resolve in the image, you see a clearer image.

Imagine you had a screen with 16 holes in it, each hole one cm apart - you cant see much detail of something behind the screen. Now imagine that screen has 256 holes in the same area - the holes are now 1/16th of a cm apart, you can see much more detail. Because more cones are receiving information.

In the eye, the magnified image is spread over many more sensors, providing a clearer image. If your eyes had 16 times as many cones in your fovea, the bit where detailed vision and colour vision occurs, the view would be a lot sharper and finer details would be resolved in your normal vision.

Camera manufacturers and camera reviewers test how sharp a lens or camera is by photographing a chart with sets of fine lines on it, with the lines being closer together in each set. How close together the lines are and still visible as separate lines is the measure of how sharply the camera resolves fine details, which can also be improved by having a bigger sensor with more sensors on it. The original data is all there all the time, it is not always resolved as separate lines. In a camera or in your eye.

 

[grindagrom]

I found this helpful
https://opticsmag.com/how-does-a-magnifying-glass-work/

The eye normally receives parallel beams of light from the target, those directly in front of the eye enter it and the eye's lens brings them to focus on the retina. Other rays not travelling directly at the the eye don't enter it.

As you can see in the diagram on that page referenced above, light that would not enter the eye - the parallel rays that end up hitting the skin above, below, to the left or the right - are bent round (refracted) by the lens and enter the eye, where they then get focused on the retina, producing a bigger image that you'd see without the lens.

Tracing back from the image on the retina to where the object appears to be (it's called a virual image) shows that the object would have to be bigger to form the same sized image on the retina. So it appears bigger.

I admit the optics wasn't my top topic in physics, as it required us to copy diagrams from the board accurately and our lecturer back then simply didn't give us enough time (deliberately, we all suspected, after he got replaced by a human being - he had a nervous breakdown from teaching us) so my notes where usually incomplete, which doesn't help anyone learn. Handouts with good diagrams back then were just not normally given to students. WWW means you can find them and study them to see what they mean.

So study the diagram and you will see what is happening to the light.

In the case of a star, the target star is occupying a tiny TINY area of your field of vision, so forms a tiny image in the eye. With a telescope or binoculars, many more light rays are refracted and give the bigger virual image that you see. The lens on the telescope or binoculars are much bigger than your eye's lens.

Ok. More or less I got it. But some questions remained. The lens is larger than the eye so it collects more light. But there are binoculars with lenses of different sizes but which give the same magnification. This leads to the second issue: the lens system. If it all comes down to lens size and amount of light, then how does the lens system affect that? The amount of light is different (in the case of different lens sizes), but thanks to the lens system, we get the same magnification

 

[grindagrom]

A star is a bad example because it looks like a point of light either way. A planet, or the moon as in @Ibix's example, is better. The fact that you can see more detail when "zoomed in" is primarily due to the resolution of your eye. The "information" is spread across more rods and cones.

And all the same about the star. I think it's interesting. A star that is billions of light years away emits rays of light. These rays diverge in all directions. How much of this light will reach the Earth? But even such a small Hubble telescope can give us a huge amount of information about this star. The diameter of its mirror is only 2.4 meters. In my opinion, only individual photons of this star should reach it.

 

[malawi_glenn]

How much of this light will reach the Earth?

Use the inverse square law

 

[hutchphd]

In my opinion, only individual photons of this star should reach it.

If you actually wanted an answer you could actually calculate the "number of photons" involved, rather than idly speculating..

 

[russ_watters]

And all the same about the star.

No, it isn't. The star is zero angular size, still covering only one rod/cone even through a telescope.

A star that is billions of light years away emits rays of light. These rays diverge in all directions. How much of this light will reach the Earth? But even such a small Hubble telescope can give us a huge amount of information about this star. The diameter of its mirror is only 2.4 meters. In my opinion, only individual photons of this star should reach it.

Hubble can't see individual stars from billions of light years away, only galaxies. But yes, it would capture single digit photons per second at most from a star that far away. We can calculate that...

 

[hutchphd]

The number I carry in my head is that Polaris, with good viewing conditions, will put less than a million "visible photons" into your eyeball per second. Since Polaris is a few hundred light years from earth this comports with @russ_watters assessment.
The OP needs to understand the difference between optical resolution and information in a modulated signal. In this context they are very different.

 

[Drakkith]

The lens is larger than the eye so it collects more light. But there are binoculars with lenses of different sizes but which give the same magnification. This leads to the second issue: the lens system. If it all comes down to lens size and amount of light, then how does the lens system affect that? The amount of light is different (in the case of different lens sizes), but thanks to the lens system, we get the same magnification

Lens size determines how much light it gathers. The focal length of the lens determines its magnification. I can take my telescope and block out the outer 50% of the aperture and it will still have the same magnification.

A star that is billions of light years away emits rays of light. These rays diverge in all directions. How much of this light will reach the Earth? But even such a small Hubble telescope can give us a huge amount of information about this star. The diameter of its mirror is only 2.4 meters. In my opinion, only individual photons of this star should reach it.

Stars are bright. VERY bright. They are very nearly the brightest things in the universe after all. Only beaten by stellar and cosmological events like supernovas and quasars.

Hubble can't see individual stars from billions of light years away, only galaxies.

To clarify for the OP, Hubble and other large telescopes can't resolve individual stars except for very large stars that are very close, such as Betelgeuse.