Eclipse reminded me what telescopes actually do

[Satchmo]

I observed the eclipse last night with a 6" F8 refractor.

Initially I was dissapointed with the view : the colours were not as bright as I could see with the naked eye. That is until I lowered the magnification enough to give a 5mm pupil at which point the colour looked as intense and bright as my unaided view. This got me thinking about why and I was reminded of something that is a little understood fact about telescopes.

Telescopes don't actually make anything appear brighter than with th enaked eye, they only magnify.

This is counter-intuitive when we think about telescopes but its true.

The surface brightness of say, the Orion Nebulae, assuming we have matched the exit pupil of the telescope to match our eye pupil diameter, is just as bright in a 24" scope as it appears to the naked eye, but of course it is much magnifies in the 24" scope.

The whole thing can be understood by taking into acount Issac Newton's inverse square law of light...

Lets say for simplicity we have a 6mm pupil on our eye . If we magnify the Orion Nebulae by 100 X with a scope of only 6mm aperture , its surface brightness will decrease by 100 squared or 1/10,000. How do we regain the brightness of the nebulae at X100 to equal the naked eye view? By increasing the surface area of our light collecting area by 10,000X. This corresponds to an increase in optical diameter of X 100 to 600mm ( 24" aperture ) !

Bang...this basic application of Newton's law then gives us the well known formula Aperture / Exit pupil = magnification and also Exit pupil ( mm ) X magnification = magnification. In this case aperture of 600mm / 6mm pupil = 100X magnification ...So the rule is , regardless of aperture if you choose the right magnification to give a maximumum pupil to match your eye , the image will be at least as bright as your naked eye.

So how are faint galaxies brought to visibility by a large telescope? If the brightness of objects is fixed for given pupil diameter , why can't we see faint galaxies with the naked eye. I think its because the eyes resolution is extremely poor in low light ( maybe a few degrees angular compared to 4 arc minutes in bright light). The magnification of a large telescope , whilst retaining the image brightness also increases the angular size of faint objects. 120 X magnification would be the minimum to enlarge the smallest galaxies of only 1 arc minute actual angular size , to 2 degrees apparent size , at which point they will suddenly pop into view. For a 6 mm pupil this is going to take 6 X 120 or 720mm of aperture. So it is the magnification that brings galaxies into view and this is made possible by maintaining the 6mm pupil with that large aperture. Hence the suitability of large apertures for detecting the smallest galaxies.

For point sources like stars , why does a large telescope make them more visible? I think it has to do with the physiology of the eye , and the fact that stars don't appear as mathematical points but small discs, which again are subject to the inverse square law of light. Perhaps someone else can carry the though experiment further on that one.

Hope people enjoy this idea and it gets you thinking.

[davewaldo]

I do like to think about these things :) ... however.

I'm not sure if I agree with this statment.

"Telescopes don't actually make anything appear brighter than with the naked eye, they only magnify."

I'm no expert, but you say that surface brightness will stay the same with different telescopes, this may be true if you compare a large telescope plus high magnification and a smaller telescope with small magnification. But isn't this bias? A larger telescope captures more light and produces a brighter image. Whether you decide to use higher magnification and therefore spread that light out again I think is up to the user. When your eye, a small scope and a large scope are all compared on equal terms, where all variables are the same ie. magnification, FOV etc. The images are brighter as you increase aperature.

I find your other points about resolution and visibility very interesting and I will continue to ponder these.

[Satchmo]

Thanks for considering and allowing me to rephrase things perhaps it will be clearer.

Yes the images *are* brighter as you increase aperture, but so does the minimum magnification needed increase, to get all of the light of the mirror into your eye. Lowering the magnification increases the exit pupil diameter, and beyond 6mm or so the light is just wasted. So its a kind of relationship you can't escape unless you are doing astrophotograghy. A good understanding of the concept of the exit pupil in a telescope then perhaps best to brush up on that or you won't follow the concepts I offer here.

So to recap : Given the limitations of our eye pupil ( lets say 6mm diameter for example) , every telescope has a magnification at which the image appears *just as bright* as the naked eye. This magnification is ( aperture in MM ) / Exit pupil ie 6mm. In the example I gave below, this is 100X for a 600mm aperture scope. if we use more magnification , then the exit pupil pupil and view becomes *dimmer* than the naked eye view. So every telescope will need a miniumum magnification of around 4X per inch to get all its light into the human eye.

The reason that the larger telescope doesn't give us a * brighter* image is that exit pupil and magnification are inextricably linked to the aperture. In order to get the light of a 600mm mirror into our 6mm pupil we must use 100X magnification, an action which reduces the surface brightness of the image by 10,000 times at the aperture of the naked eye, but we win back the light intensity by pumping the light of a mirror with 10,000 X the surface area of our pupil into the pupil ( a 600mm diameter mirror ! ). It all goes back Newton's inverse square law of light.

Heres another simple thought experiment. Imagine we put a star diagonal into the newtonian and angle it so we can look at the rising full moon both with one unaided eye and through the scope. Now pulling our eye back so the angular field is more and more reduced, until all we can see of the full moon through the scope is a disc subtending about 1/2 degree in aparent diameter. We now find that regardless of the telescope aperture , the Moon will look the same brightness when we compare the naked eye view to the small piece of the lunar surface we can see with the head pulled way back from the eyepiece:) And yet the Moon 'seems' brighter when we put our eye up to the eyepiece, simply becasue there is som much more surface area to dazzle our eye becasue the telescope's magnification has given the Moon a much larger apparent angular size in our field of view !

Telescopes used for photograpghy , don't have the exit pupil limitation and for a given focal length you can pump in as much light as you wish depending on how much money you have to spend :)

The very reason this topic came up is because I know how the eye must have X amount of light hitting the cones ( ?) for colour sensitivity to activate, and it was only when I bumped my scopes pupil up to 5mm that th e colour intensity matched the naked eye view , so I know the brightness * per unit of angular view* must have approached the same between the naked eye view and telescopically.

I brought this subject up as it is a fascinating one, that is so counter -intuitive and will change the whole way you think about your telescope ;-) Obviously the increased aperture gives you increased resolution but that is a different subject altogether .

Limiting magnitude of stars ( point sources ) is something that varies with the seeing and has more to do with resolving power I think, this is what I would like to delve into understanding further.

[davewaldo]

This is quite fascinating, thanks for posting. I now better understand your point.

Like you say it is quite counter intuitive, I come from a pro photography background and deal with inverse square law every day. I forget about the limitations of our eye. I was over simplifying things in my head - Scope = Lens, Eye = Camera. But now I understand better.

Cheers! :) I like pondering these concepts!