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# Magnitude question.

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### #1 Guest_**DONOTDELETE**_*

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Posted 08 March 2004 - 07:32 PM

If the were three separate telescopes with equal magnifications set up A, B, and C and the light gathering power for each was as follows:

A = x
B = 2x
C = 4x

Would the gain in magnitude from A to B be the same a the gain from B to C? Against a completely black sky I know that in theory they would, but what if there is light pollution, is the relationship still linear(in theory)?

### #2 EdZ

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Posted 08 March 2004 - 08:03 PM

NO. And the answer to knowing that they would in theory under a dark sky have the same gain is dependant on the magnification in use and could also be NO.

At magnifications less than optimum the relationship is not so linear as you might think.

edz

### #3 Guest_**DONOTDELETE**_*

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Posted 08 March 2004 - 08:50 PM

Thanks Ed.

### #4 Guest_**DONOTDELETE**_*

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Posted 08 March 2004 - 09:07 PM

I have another question. What kind of range in brightness can a light polluted sky have- what's the sky's surface magnitude?

[Edited the rest out]

### #5 Guest_**DONOTDELETE**_*

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Posted 08 March 2004 - 10:38 PM

Edit:

I need to do a little research before I ask my next question. I edited this and the last post because my question wasn't very clear.

### #6 sftonkin

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Posted 09 March 2004 - 01:00 AM

There are several things going on at once here. The most important are:

* For point objects, larger apertures concentrate the light into smaller Airy discs at the focal plane than does a smaller aperture at the same focal length. Because the Airy disc is smaller, it is more intense, and is therefore relatively brighter in the eyepiece, given the same magnification. Because it is the radius of the Airy disc that is inversely proportional to the aperture, the area of the Airy disc is an inverse square function of the aperture and hence the intensity of the disc is proportional to the area of the aperture.

* No passive optical system can increase the brightness of an extended object. When you increase the magnification by, say, M, you increase the illuminated part of the retina by M², so the intensity of light falling on each receptor decreases as an inverse square function of magnification. If we magnify until the Airy disc is the same intensity as in the smaller instrument, the background sky (i.e. an extended object) will be proportionately darker, so we have increased contrast.

Then you have (for refractors, i.e. most binoculars) the relatively higher proportion of light absorbed by the thicker lenses of the larger instrument, the increased chromatic aberration of a scaled up refractive system pushing a higher proportion of energy outside the Airy disc (a 100mm f/5 objective has far more chromatic aberrationthan a 50mm f/5 of the same design), and the non-linear response to light intensity of our visual system.

As you can see (and as you probably already knew), the answer to your questions is non-trivial. Some of this is covered in a bit more detail on my short web tutorial on Telscope Function: http://astunit.com/t...s/telescope.htm

I hope this helps more than it confuses.

### #7 wilash

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Posted 09 March 2004 - 03:42 AM

Stephen,

Got a question for you. The relative intensity of the Airy disk increases with aperture. Doesn't the intensity also vary with magnification?

### #8 Guest_**DONOTDELETE**_*

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Posted 09 March 2004 - 12:37 PM

Thanks a lot Stephen!

### #9 sftonkin

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Posted 09 March 2004 - 05:32 PM

Yes. Covered in the second asterisked point.

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