Why are maginification and exit pupil values not related to AFOV

[keybaud]

I'm trying to get my head around eyepiece maths, but one bit has me confused.

Magnification = telescope focal length/eyepiece focal length

Exit pupil = telescope aperture/magnification

This implies that two eyepieces with same focal length, but different AFOVs have the same magnification and the same exit pupil, but this is physically impossible. Surely, a wider field of view will be less magnification for the same exit pupil size or a larger exit pupil for the same magnification.

What have I missed?

[keybaud]

I may have just answered my own question. I assume that the exit pupil is actually the smallest diameter the light passage passes through; however a wide FOV eyepiece will accomodate steeper entrance and exit angles, so it will give a 'bigger' image on the retina for the same exit pupil.

[JED-E3]

You can have two eyepieces with the same magnification but different fields of view.

The magnification dictates the size of the object you see, the apparent field of view dictates how much extra you see around the object.

If you look down a cardboard tube the magnification is the same, but the field of view is smaller.

[keybaud]

You can have two eyepieces with the same magnification but different fields of view.

The magnification dictates the size of the object you see, the apparent field of view dictates how much extra you see around the object.

If you look down a cardboard tube the magnification is the same, but the field of view is smaller.

A cardboard tube is a smaller exit pupil, though, hence my initial confusion.

[NGC 1502]

Maybe this will explain -

I have a 10mm TV Radian eyepiece.  With my 10" Dob, magnification is 120x.  The 60 deg field shows 0.5 degrees of sky (60 / 120 = 0.5), exit pupil is 250 / 120 = 2.08 mm.

If I had a 10mm TV Ethos that would give the same magnification and the same exit pupil.  But I'd see more sky (100 / 120 = 0.83 degrees).

So a wider field of view will not alter the magnification or the exit pupil, the difference is how much sky is seen.

The other effect of the Ethos is a smaller bank balance 

The cardboard tube analogy in post # 3 is a simpler way of saying the same.

Regards, Ed.

[Mr Spock]

Your logic is flawed The exit pupil has nothing to do with fov of the eyepiece.

To calculate exit pupil, divide the focal length of the eyepiece by the f ratio of the scope. For example, a 25mm eyepiece in a f5 scope will have an exit pupil of 5mm. A 10mm eyepiece in a f10 scope will have an exit pupil of 1mm.

Or, you can divide the aperture by the magnification. For example, a 150mm scope at x100 will have an exit pupil of 1.5mm.

[Tiki]

What have I missed?

The field stop diameter?

[AlexB67]

FWIW, another way of looking at it. Aperture gathers light and results in an exit pupil, but think of light in this case as photons or like a flux,  an amount going through a slab of unit area. You can have a larger total area (FOV ), but the amount coming through per unit area is the same regardless, and therefore independent of it.

If I plant grass in my garden, suppose a  perfect Wimbledon lawn with one blade per square cm. Whether my lawn is 20 m² or 40 m², it has no bearing on the fact that I still have one blade of grass per square cm.

[keybaud]

I have a 10mm TV Radian eyepiece.  With my 10" Dob, magnification is 120x.  The 60 deg field shows 0.5 degrees of sky (60 / 120 = 0.5), exit pupil is 250 / 120 = 2.08 mm.

If I had a 10mm TV Ethos that would give the same magnification and the same exit pupil.  But I'd see more sky (100 / 120 = 0.83 degrees).

My question was effectively, why do you see more sky, which I think I answered in my second post. I was assuming the exit pupil was the image size, but it isn't. It is the minimum aperture the light is coming through and the light will be at a steeper angler with a wide FOV eyepiece.