What is the role of focal lengths in ray diagrams for telescopes?

[Jimmy87]

When you look up a ray diagram for a telescope you get the following:

From reading my book it seems clear that the objective lens forms and image on the focal plane. This then serves as an image for the eyepiece. Since the focal length of the eyepiece at the focal length of the objective lens you get a virtual image at infinity. Three questions have come to me:1) I didn't think you could get an image at infinity since the light rays do not converge?

2) Different sources tell me different things about the focal lengths. This source says right at the beginning that for a telescope the focal lengths actually overlap:

3) I really don't get why the image from the objective lens is sometimes in the focal plane as oppose to the focal point. In the diagram above the light rays (although parallel) come in at some angle to the principle axis. When could this ever happen because surely you just point your telescope straight at the object you are looking at in the sky so that the rays will always be parallel to the principle axis? But then if they did am I right in saying that you would get no image as the rays would all converge to a point right at the focal point?

Thanks for any help given!

 

[lychette]

the image formed by the objective lens is the OBJECT for the eyepiece lens.
The parallel rays entering the objective are from the top of the object at infinity. Look at the arrow which is the image. The base of the image is at the focal point. This is the point where rays parallel to the axis meet.

 

[Jimmy87]

the image formed by the objective lens is the OBJECT for the eyepiece lens.
The parallel rays entering the objective are from the top of the object at infinity. Look at the arrow which is the image. The base of the image is at the focal point. This is the point where rays parallel to the axis meet.

Thanks. I understand all of that what I don't understand is the FINAL image after the image formed by the objective lens has gone through the eyepiece. If you trace back the rays from the final image they do not converge and it says that the image is formed at infinity - is they do no converge and form an image at infinity then how does this form an image?

 

[Drakkith]

Thanks. I understand all of that what I don't understand is the FINAL image after the image formed by the objective lens has gone through the eyepiece. If you trace back the rays from the final image they do not converge and it says that the image is formed at infinity - is they do no converge and form an image at infinity then how does this form an image?

The rays enter your eye and the eye makes them converge on your retina. Because the rays were parallel when the entered your eye, the image appears to be an infinite distance away. But really, when we say the image is 'formed at infinity' we just mean that the rays from any point on the image are parallel/near-parallel. A star that's 5,000 light-years away doesn't actually emit rays parallel to themselves, but they are so close to parallel that we can treat them as parallel for almost all purposes.

3) I really don't get why the image from the objective lens is sometimes in the focal plane as oppose to the focal point. In the diagram above the light rays (although parallel) come in at some angle to the principle axis. When could this ever happen because surely you just point your telescope straight at the object you are looking at in the sky so that the rays will always be parallel to the principle axis? But then if they did am I right in saying that you would get no image as the rays would all converge to a point right at the focal point?

If you point your telescope at the Sun, right at the middle of the Sun, then only the rays from the middle of the disk will be focused to the 'focal point'. The rest of the disk will be focused at points an increasing distance away from the focal point. Together, these points make up the focal plane. Except for the rays from the middle of the Sun's disk, the rays will all enter the telescope at an angle to the principle axis.

 

[davenn]

If you point your telescope at the Sun, right at the middle of the Sun,

and for the OP's benefit in case he doesn't realize
but don't do that unless you use appropriate solar filters

 

[Jimmy87]

The rays enter your eye and the eye makes them converge on your retina. Because the rays were parallel when the entered your eye, the image appears to be an infinite distance away. But really, when we say the image is 'formed at infinity' we just mean that the rays from any point on the image are parallel/near-parallel. A star that's 5,000 light-years away doesn't actually emit rays parallel to themselves, but they are so close to parallel that we can treat them as parallel for almost all purposes.
If you point your telescope at the Sun, right at the middle of the Sun, then only the rays from the middle of the disk will be focused to the 'focal point'. The rest of the disk will be focused at points an increasing distance away from the focal point. Together, these points make up the focal plane. Except for the rays from the middle of the Sun's disk, the rays will all enter the telescope at an angle to the principle axis.

Thanks, you have been very helpful. If the rays enter the eye parallel and the image is at infinity then surely you haven't magnified the image? So what is the point of such a set up? If you actually do get an image under these conditions then how would you draw it on a ray diagram such as the one in my original post.

One other thing that is really bothering me is when people say that the eye sees objects coming from the same line of sight as the rays entering the eye. This explains refraction as shown in this diagram:

However, the eye will converge the rays shown in this diagram onto the retina as you say. Am I therefore correct in saying that light enters your eye, gets refracted by your lens onto the retina which relays the message to your brain. Your brain is able to infer the location of the object BEFORE the light got refracted by the lens and does this by assuming that it came along the same line as it entered the eye whether or not this is the case (as it wouldn't be in the case of refraction). It just seems weird that the message to your brain gets sent after refraction from the lens but it can tell the location of the object using information before it got refracted?

 

[sophiecentaur]

3) I really don't get why the image from the objective lens is sometimes in the focal plane as oppose to the focal point. In the diagram above the light rays (although parallel) come in at some angle to the principle axis. When could this ever happen because surely you just point your telescope straight at the object you are looking at in the sky so that the rays will always be parallel to the principle axis? But then if they did am I right in saying that you would get no image as the rays would all converge to a point right at the focal point?

This may be obvious but it has to be said; the purpose of a telescope is to Magnify the angle between two distant points (two point stars or two sides of a resolvable object). only a small proportion of rays come directly along the principle axis and the rest arrive from a bit to one side (perhaps only minutes of arc). Diagrams of telescopes exaggerate the angles so that you can actually see the plotted rays. The magnification in a simple telescope is given by the ratio of the focal lengths of the objective and eyepiece lenses. A magnification of only 60X will take an pobject that's 1minute of arc and give you an image that's still only 1 degree wide. You would need to be pointing pretty damn close to an abject in order to see it because the field of view is so small. Perhaps that explains your dilemma?

 

[Drakkith]

Thanks, you have been very helpful. If the rays enter the eye parallel and the image is at infinity then surely you haven't magnified the image? So what is the point of such a set up?

Whether the rays enter the eye parallel to themselves or not is a matter of focus, not magnification. When focusing a telescope you are supposed to move the eyepiece in or out until the rays enter your eye parallel to each other. At this point your eye doesn't need to use your lens to focus at all since the image seems to come from infinity. If you move it to a sub-optimal position, you have to use your lens to focus the now diverging cone of light onto your retina, which leads to eye strain and causes the image to seem as if it is closer than infinity.

Am I therefore correct in saying that light enters your eye, gets refracted by your lens onto the retina which relays the message to your brain. Your brain is able to infer the location of the object BEFORE the light got refracted by the lens and does this by assuming that it came along the same line as it entered the eye whether or not this is the case (as it wouldn't be in the case of refraction). It just seems weird that the message to your brain gets sent after refraction from the lens but it can tell the location of the object using information before it got refracted?

Your brain simply uses the position of the image on your retina (among several other ways unrelated to ray optics) to determine where an object is. Your brain has little to no way of knowing whether the image is actually an optical illusion or not.

 

[Jimmy87]

Whether the rays enter the eye parallel to themselves or not is a matter of focus, not magnification. When focusing a telescope you are supposed to move the eyepiece in or out until the rays enter your eye parallel to each other. At this point your eye doesn't need to use your lens to focus at all since the image seems to come from infinity. If you move it to a sub-optimal position, you have to use your lens to focus the now diverging cone of light onto your retina, which leads to eye strain and causes the image to seem as if it is closer than infinity.
Your brain simply uses the position of the image on your retina (among several other ways unrelated to ray optics) to determine where an object is. Your brain has little to no way of knowing whether the image is actually an optical illusion or not.

Thanks again! In ray diagrams I have seen you physically trace the rays back until they converge and you then get the size and orientation of the image. For example:

Why can't you do this for the one I posted at the start? Since the image formed by the eyepiece will be bigger than the one formed by the objective lens wouldn't it?

Which configuration do telescopes actually use because there seems to be one when the focal length are matched as shown above and ones were they overlap so that the image is more magnified like this one:

 

[lychette]

you can do this ! A magnifying glass operates like this. The image is virtual. The eye is most comfortable viewing parallel light rays therefore the most comfortable arrangement (especially in astronomy) is to have the 'image' at infinity.
You need to realize that whatever arrangement of lenses in the telescope/microscope the final image is on the retina of your eye...There is a lens in your eye !
Also, I think sophicen... mentioned it...the magnification is an angular magnification, the angle of the light entering your eye from the telescope is greater than the angle without the telescope (even though both images are at 'infinity')

 

[Merlin3189]

When focusing a telescope you are supposed to move the eyepiece in or out until the rays enter your eye parallel to each other. At this point your eye doesn't need to use your lens to focus at all since the image seems to come from infinity. If you move it to a sub-optimal position, you have to use your lens to focus the now diverging cone of light onto your retina, which leads to eye strain and causes the image to seem as if it is closer than infinity.

As a myope I would have to disagree. Unlike people with normal vision, whose eye lens focuses parallel rays to form an image on their retina, my eye lenses focus parallel rays rather short of my retina producing a blurred image. To see objects distant enough for their rays to be near parallel, I wear spectacles (eye glasses) to produce a virtual image about 40cm away from my eye. My eye lens can then focus the light from this to form a sharp real image on my retina. When I use a telescope, microscope or binoculars, I adjust the eyepiece to similarly produce a virtual image at 40cm, as shown in the second diagram. Using my eye lenses to focus diverging rays does not cause me eyestrain any more than a normal person using his eye lenses to focus parallel rays. (*)

I am not aware of the images I view through a telescope being any closer than infinity. The rays that enter my eye require exactly the same focusing as the rays I see from any distant object when wearing spectacles.
But it is interesting that in everyday life, when wearing specs, distant objects do not seem closer. I think this must be due to the fact that eye lens focus is either not a cue to depth perception at all, or is a very minor cue. And even though they are concave lenses, I am not aware that objects look smaller, even at the moment of first putting them on. (I think this is the point about angular magnification made by SophieC.)

(*) Incidentally, I wonder why using ones eye lenses to focus rays should ever cause eyestrain? Does reading normally cause eyestrain? Most people do not use spectacles to enable them to read using parallel rays. I also suffer from presbyopia, so I do, but most young people do not. My guess is that eyestrain - if indeed the condition exists - is more likely caused by looking at unclear images, where the eye is continually refocusing in a vain attempt to clarify the image. If a sharp image can be obtained somewhere between your near point and your far point, then think neither parallel nor divergent rays should cause any problem.

 

[Drakkith]

Why can't you do this for the one I posted at the start? Since the image formed by the eyepiece will be bigger than the one formed by the objective lens wouldn't it?

Yes. In fact, I can easily change the magnification of my telescope just by changing out the eyepiece. Note that a telescope, consisting of an objective lens and an eyepiece, is a complex optical system, not a simple one like a magnifier. The object the eyepiece is viewing is actually the image formed by the objective lens. The eyepiece acts as a short focal length magnifier for the image produced by the long focal length objective. Since you typically focus the telescope so that rays entering your eye are nearly parallel you can't just trace the rays back to their point of convergence (since there isn't one for parallel rays).

Which configuration do telescopes actually use because there seems to be one when the focal length are matched as shown above and ones were they overlap so that the image is more magnified like this one:

That I don't know.

As a myope I would have to disagree. Unlike people with normal vision, whose eye lens focuses parallel rays to form an image on their retina, my eye lenses focus parallel rays rather short of my retina producing a blurred image. To see objects distant enough for their rays to be near parallel, I wear spectacles (eye glasses) to produce a virtual image about 40cm away from my eye. My eye lens can then focus the light from this to form a sharp real image on my retina. When I use a telescope, microscope or binoculars, I adjust the eyepiece to similarly produce a virtual image at 40cm, as shown in the second diagram. Using my eye lenses to focus diverging rays does not cause me eyestrain any more than a normal person using his eye lenses to focus parallel rays. (*)

Obviously my description above only applies to folks with normal vision and not you and I that are nearsighted.

I am not aware of the images I view through a telescope being any closer than infinity. The rays that enter my eye require exactly the same focusing as the rays I see from any distant object when wearing spectacles.
But it is interesting that in everyday life, when wearing specs, distant objects do not seem closer. I think this must be due to the fact that eye lens focus is either not a cue to depth perception at all, or is a very minor cue.

Indeed. Humans generally don't gauge distance using focus. An image that is 'focused at infinity' is one that doesn't require you to exert effort to bring the object into focus. For us nearsighted folks this means that the rays entering our eyes aren't actually parallel, but are diverging slightly.

And even though they are concave lenses, I am not aware that objects look smaller, even at the moment of first putting them on. (I think this is the point about angular magnification made by SophieC.)

That's right. Eyeglasses aren't typically strong enough to cause any noticeable magnification change. I think this may have something to do with the eye being well inside the focal length of the lens, but I'm not sure.

(*) Incidentally, I wonder why using ones eye lenses to focus rays should ever cause eyestrain? Does reading normally cause eyestrain?

As far as I know it does. And the closer the reading material is to your eye, the harder you have to focus and the quicker you'll tire your eye out. Try reading a book that's 2-3 inches from your face for more than a minute or two. You'll feel it.

Most people do not use spectacles to enable them to read using parallel rays.

Well, if they did, then anything further away than the book would appear blurry since your eye wouldn't be able to bring those rays into focus. Most people expend a small/moderate effort to bring the diverging rays from the book into focus instead of having a set of eyeglasses that they'd have to take off every time they look up. Although, now that I think about it, reading glasses may do this to some extent. I've tried my parents' reading glasses on before. I can't see anything far away at all. It's like looking through a magnifying glass (which is essentially what reading glasses are).

My guess is that eyestrain - if indeed the condition exists - is more likely caused by looking at unclear images, where the eye is continually refocusing in a vain attempt to clarify the image. If a sharp image can be obtained somewhere between your near point and your far point, then think neither parallel nor divergent rays should cause any problem.

The condition is real. It's called asthenopia.
More references and information:
http://eyewiki.aao.org/Asthenopia
http://www.eyehealthweb.com/eye-strain/
http://vision.about.com/od/eyediseasesandconditions/g/Asthenopia.htm
http://www.ncbi.nlm.nih.gov/pubmed/14627938

Note that the sustained effort of focusing on nearby objects is only one cause of asthenopia.

 

[Jimmy87]

Yes. In fact, I can easily change the magnification of my telescope just by changing out the eyepiece. Note that a telescope, consisting of an objective lens and an eyepiece, is a complex optical system, not a simple one like a magnifier. The object the eyepiece is viewing is actually the image formed by the objective lens. The eyepiece acts as a short focal length magnifier for the image produced by the long focal length objective. Since you typically focus the telescope so that rays entering your eye are nearly parallel you can't just trace the rays back to their point of convergence (since there isn't one for parallel rays).

Thanks again for being so helpful. So is the way they teach you not strictly correct then because I am taught that for a magnifying glass for example you trace the rays back behind the glass to see the type of image you would get. Or is it still true but when you have a situation where they do not converge it doesn't mean you won't get an image it just means you can't use that method?

Would someone be so kind as to check an answer for a question we did in class (well actually I answered the question and its more of an extension of the question I was wondering about). We had to answer this question:

And my answer (which was correct) was:

But am I right in thinking that this is the image from the objective? Is it actually an accurate situation - can you get light coming from the top and bottom like this? I was wondering how you would go about drawing the rays through the eyepiece if I was ever asked. Would it be something like this:

 

[Drakkith]

Thanks again for being so helpful. So is the way they teach you not strictly correct then because I am taught that for a magnifying glass for example you trace the rays back behind the glass to see the type of image you would get. Or is it still true but when you have a situation where they do not converge it doesn't mean you won't get an image it just means you can't use that method?

I'm not an expert on this topic, but it seems to me that while for a simple magnifier that method works fine, you might not be able to use it for a complex optical system involving multiple elements such as this one.

But am I right in thinking that this is the image from the objective?

That's right.

Is it actually an accurate situation - can you get light coming from the top and bottom like this?

Absolutely. If you put a camera sensor at the focal plane of the objective, the light would be focused directly onto the sensor's pixel array. That it exactly how prime-focus astroimaging is done.

I was wondering how you would go about drawing the rays through the eyepiece if I was ever asked. Would it be something like this:

Yes it would be. This matches the diagram you posted in your first post.

 

[sophiecentaur]

But am I right in thinking that this is the image from the objective? Is it actually an accurate situation - can you get light coming from the top and bottom like this? I was wondering how you would go about drawing the rays through the eyepiece if I was ever asked. Would it be something like this:

Yes, more or less. The real intermediate image will extend on either side of the principal axis (as you have drawn) and the virtual, final image will appear to be where those final pairs of rays ( appear to be diverging from (draw dotted lines, extending way over to the left) at infinity and subtenting a much greater angle. But it isn't necessary to have an image extending either side of the axis- it is sufficient to go from the axis to one side. After all, that would only corresponding to pointing the scope slightly up or down.

 

[Drakkith]

But it isn't necessary to have an image extending either side of the axis- it is sufficient to go from the axis to one side. After all, that would only corresponding to pointing the scope slightly up or down.

While true, I'd like to point out that the 'image' will consist of anything within the field of view of the telescope, not just a single object. This seems so obvious as to make mentioning it pointless, but I feel many people are too deep down into the details to realize it when they first start studying optics.

 

[sophiecentaur]

While true, I'd like to point out that the 'image' will consist of anything within the field of view of the telescope, not just a single object. This seems so obvious as to make mentioning it pointless, but I feel many people are too deep down into the details to realize it when they first start studying optics.

Agreed. In an astronomical telescope the 'object' will often be two stars, next to each other. The magnification factor will apply to that separation or that of any two parts of the input field. The nice thing about an 'Arrow' to denote an object or image in optics is that it is independent of what the actual object might be.