Keplerian telescope

I don't understand what my book is talking about:

I thought that converging telescopes do make distant objects look bigger via the eyepiece lens (magnifies the image produced at the focus from the objective lens). So why does the book say otherwise?


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The answer the book gives needs to be qualified because the quality of the lenses in any given telescope will have a dramatic effect on what you see:

There are a few parts to this, but at high magnifications, the most important is the resolving power of the lens which is the ability to separate fine detail.

Since stars are an enormous distance away, most telescopes (other than large arrays that governments struggle to afford) cannot resolve that level of detail. Magnifying the image won't produce any more detail. The image will be still be fuzzy.

Objects closer to the telescope are not a problem. i.e. planets, or very large objects far away like galaxies which are tens of thousands of light years wide.

Resolving power only becomes an issue when other factors (which are dominant in cheaper telescopes) swamp resolving power long before it becomes an issue; like, the image won't be bright enough to see in the first place! :

A telescope can only gather a fixed amount of light which depends on the diameter of the objective lens/mirrors. i.e. size of the objective lens determines how bright the image will be. The bigger the objective the more light is gathered.

This is because when using high magnification the gathered light is spread over a larger area. (logical as the image is larger but the light gathered has not changed). So as the magnification goes up, the brightness of the image you see goes down. At some high magnification your eye simply won't see the image - it will still be there but too dark for you to see.

So the useful magnification has a limited range determined by the objective lens diameter. A guide is around 60x for every inch diameter. So a 5" telescope will have a useful maximum magnification of around x300. A 3" telescope would be x180. (Sales adverts which says a 2" telescope has a magnification of x500 are utterly ridiculous - beware).

The second factor is the focal length of the telescope. i.e. the distance the objective lens needs to bring that light into focus. The objective focal length will determine how long the telescope needs to be: the telescope tube has to hold the lenses at those positions after all.

Then there is the eyepiece lens which itself has both a diameter and a focal length.

The actual magnification you are using is simply the larger lens diameter divided by the smaller lens diameter. So a 800mm objective focal length divided by a 20mm eyepiece focal length operates at 40x magnification.

This says another important fact: Telescopes with long focal lengths can reach higher magnification.

So there's the catch. As the magnification increases not only does the image get dimmer but the area you can see gets smaller because of those focal length ratio's. And, even if you could get a telescope with a huge objective lens diameter to gather as much light as possible (say several metres diameter, the resolving power of the lens means you may not see enough detail anyway).

It's all a compromise.

Bit of a long answer, but as you see the explanation the book needs to give is missing for that reason!

Thank you so much (defo REP) !!

I got a few questions regarding your answer:

1) How is resolving carried out in a telescope (are the lenses in the telescope adjusted until they form a sharp image?)

2) So fundamentally if you magnify the image of a distant object (via increasing the aperture of the objective lens), resolution power decreases <--- why does resolving power decrease? (is this because the brightness of the image has decreased, thus the ability to see fine detail will decrease)?

3) How is magnification increased? (I understand that it's probably to do with decreasing the eyepiece's focal length, but how is this done?)

4) Could you please elaborate on the sentences I've emboldened. And in regards to the first emboldened line, is the image "fuzzy" because of the diffraction of the rays of light as it hits the edges of the lens?

5) So what will be the properties of an 'ideal' telescope to view distant objects?

I am SO SORRY about asking all these questions, but seeing as you are a God-send in telescopes, who else to ask lol?

Hi.

I'll try to answer best I can:

1) Resolving is the ability of a lens to produce separate images of two close objects. It's scientific term is angular resolution and resolution is the minimum resolvable distance measured as an angle subtended at the lens.

This resolving ability is limited either by aberration (caused by imperfections on the surface smoothness and contour of the lens which bring the light to different focal points thus causing blurring) and by diffraction which is a function of the different wavelengths of the light passing through the lens which causes slowing down and speeding up as it passes through different densities. (why prisms separate white light into colours). You can also see this effect by observing the colours formed on the surface of a CD or DVD.

So the sharpness of the image will be limited by both aberration and diffraction. If the aberration imperfection is minimised by using ultra high-quality lenses, then diffraction becomes the dominant limit as the light must always pass through the lens. But that objective lens perfection comes with a very high price tag.

2)As the objective lens diameter increases, then it's true that the image can be magnified further before running into brightness problems again. But as the lens diameter increases, then keeping the lens surface perfect becomes much harder. So the aberrations become harder to keep under control.

i.e. as the lens gets bigger, then so must it's quality to keep aberrations at bay hence to use that bigger objective diameter light gathering ability for extra magnification, the lens quality has to go up accordingly or resolution will suffer.

3) The shorter the focal length, the more powerful the lens.
But, conversely, the shorter the focal length the harder it is to keep perfect shape before those aberrations creep in.

Hence the compromise: the objective lens has a large diameter and a long focal length so not a great deal of magnification, because a large lens is easier to make if the surface curvature is not too great. It's job is to gather as much light as possible.

The light from the objective is brought to the eyepiece lens which has small diameter and short focal length because it's easier to make a small high magnification lens.

The eyepiece lens will also be composite (many lenses) to try to compensate for those omni-present aberrations.

All the light gathering is done by the large objective lens. The magnification and correction is done by the eyepiece lens.

4) See previous answers which explain.

5) It all depends on what you want to look at.

For planets the best type is a refractor of which the Keplerian is one. The objective does not need to have huge light gathering ability so magnification will be down to objective focal length and the quality of both objective and eyepiece lens'. 3" objective is a good starting point.

For deep space objects, light gathering ability of the objective lens becomes the most important factor. So a large aperture Newtonian reflector is considered the best since the magnification is not the issue (detail on stars cannot be resolved for the reasons previously given) but it's no good if you can't gather enough light to see those distant objects.
You can get a good 6 or 8" reflector for very reasonable money.

A compromise telescope is the Schmidt-Cassegrain (catadioptric) which is a compound telescope offering a much shorter tube whilst still offering the large objective diameter of the Newtonian and the benefits of of the refractor.

It's also the most expensive option for the beginner.

Thank you so much!

Words cannot express my gratitude!!!

I just got one statement, its when you were describing diffraction (emboldened above), I thought that this was the definition of refraction. And I thought that diffraction, in relation to telescopes, occurred because the long wavelengths of light coming from a distance source were being bent by the edges of the lens, thus causing distortion in the resolution of the image.

Is my thinking incorrect?

that seems like a description of chromatic abberation rather than diffraction tbh.

Really? Because wikipedia states that it is "the apparent bending of waves around small obstacles" <---- Won't this be the edges of a lenses?

yeah, you get diffraction with any apeture so it affects refractors and reflectors. Chromatic aberration only occurs in lenses. Dunno how much this is helping with your query

Thank you so much!

Words cannot express my gratitude!!!

I just got one statement, its when you were describing diffraction (emboldened above), I thought that this was the definition of refraction. And I thought that diffraction, in relation to telescopes, occurred because the long wavelengths of light coming from a distance source were being bent by the edges of the lens, thus causing distortion in the resolution of the image.

Is my thinking incorrect?

You are of course absolutely correct, my bad for typing too fast! lol.
Yes, the latter explanation refers to the former refraction statement which causes chromatic aberration whilst deviation from the ideal surface contour of the lens causes spherical aberration.

Diffraction occurs when a plane propagating wavefront of em-radiation passes through the objective opening and diverges. (in essence a wider circular version of Young's slit) The resultant wave spread produces a Gaussian intensity distribution pattern as the now different wave path lengths produce phase interference which either cancel or reinforce relative to the size of the aperture and the wavelength of the light.

I know this description is somewhat trivial, you may want to search out other sources but be warned, diffraction is classed as a phenomenon and has no generally accepted understanding of it's root cause. Theories get complicated very quickly, superpostion of secondary wavefront interference, Quantum Electro-Dynamics and hence General Relativity, tensors, you get the drift; way beyond A-level physics and further A2 maths.

Diffraction explanations in most texts are limited to a description of its effects rather than trying to understand why. The often quoted Huygens-Fresnel diffraction principle is the equivalent of Newtons gravitational laws in that it predicts behaviour but does not explain why.

But I digress. Resolving power, in essence, is the ability of the optics to differentiate the overlap in Gaussian intensity distributions (diffraction patterns) of two almost-parallel wavefronts arriving at the objective aperture and then diffracted to cause interference pattern images.

The generally accepted formula for the resolving power is 1.22*lambda/D
where lambda is the wavelength of the em-wavefront and D is the aperture diameter. This directly relates to the angle alpha between two (almost parallel) arriving wavefronts from a distant object.

To get an idea of the numbers, plug some in: say the wavelength of the arriving light is 500nm = 500x10^-9 m with an objective diameter of say 75mm = 0.075m.

Then alpha = (1.22 x 500x10^-9) / 0.075 = 0.03 arc seconds approx. This is the minimum angle of nearly-parallel light from two adjacent point sources our telescope can resolve before the images are merged to be indistinguishable from each other.

So for a distant object say Saturn, it has a diameter of 120x10⁶m and has a mean distance of say 1.5x10¹²m. which subtends an angle of 0.288 arc seconds at the objective lens: an order of magnitude within the capability of our telescope.

Meaning our 75mm objective can resolve detail down to around 12,000km at that distance. With sufficient magnification, enough to see the disc and a blurred ring but no other detail.

So now do the same for the nearest star at 4.3 light years distance:

Assuming the star is similar diameter to our sun say 1.5x10⁹m and distance is 4.3x(300x10⁶)x60x60x24x365 = 4.1x10¹⁶m which produces an angle of 0.00013 arc seconds at the objective. 2 or 3 orders of magnitude below that which our 75mm objective can resolve.

Are you like the Jesus of telescopes or something lol?

You have been an immense help for me -thank you so much.

Nah, just an engineer who has a few nerdy hobbies!

Glad I could help.

Hmmmm. Are you asking this because you are seriously interested or simply trying to be devious getting someone else to do your homework/coursework without being too obvious?

Not a very nice thing to do.