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# Exit pupil puzzle

22 replies to this topic

### #1 25585

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Posted 25 March 2020 - 04:03 PM

Using astronomy tools, a 21mm Ethos gives an exit pupil of 4.2mm in both my 10" F5 FL 1270mm and 12" F5 FL 1500mm scopes. But for my 10" F6 FL 1600mm, the exit pupil is calculated as 3.33mm.

What does the 12" F5 have same exit pupil as 10" F5?

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Edited by 25585, 25 March 2020 - 04:05 PM.

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### #2 lsfinn

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Posted 25 March 2020 - 04:10 PM

Exit pupil is equal to ep fl divided by f-ratio: it is independent of aperture.

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### #3 Dave Mitsky

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Posted 25 March 2020 - 05:02 PM

Exit pupil is also equal to aperture divided by magnification.

https://skyandtelesc...elescope-owner/

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### #4 John Huntley

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Posted 25 March 2020 - 06:17 PM

I think the answers are above.

Nice avatar choice, very nice

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### #5 russell23

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Posted 25 March 2020 - 08:42 PM

As explained above, the exit pupil can be easily calculated by dividing the eyepiece focal length by the telescope focal ratio.   A 21mm Ethos will give the same exit pupil in any f/5 scope no matter the aperture and it will give a different exit pupil in any scope with a different focal ratio.

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### #6 Jon Isaacs

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Posted 26 March 2020 - 05:31 AM

My two cents:

The exit pupil decreases as the magnification increases, this can be seen simply by swapping eyepieces.

Dave posted the equation Exit pupil = Aperture / Magnification.   I find this more intuitive than Focal length eyepiece / focal ratio but they are really the same equation.

EP = D/M

M = FLeyescope / FLeyep

EP = D/(FLscope/FLeyep)  = FLeyep x (D /FLscope)  but D/FLscope = 1/Fratio  => EP =  FLeyep/Fratio.

Jon

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### #7 Miranda2525

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Posted 26 March 2020 - 07:55 AM

Using astronomy tools, a 21mm Ethos gives an exit pupil of 4.2mm in both my 10" F5 FL 1270mm and 12" F5 FL 1500mm scopes. But for my 10" F6 FL 1600mm, the exit pupil is calculated as 3.33mm.

What does the 12" F5 have same exit pupil as 10" F5?

How do you measure the exit pupils of eyepieces to come up with exactly 4.2mm? What kind of a caliper are you using?  How can the naked eye see something that small? IMO, you need to use a digital caliper and a loupe to see that, especially when using really short FL eyepieces.

Edited by Miranda2525, 26 March 2020 - 07:58 AM.

### #8 Miranda2525

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Posted 26 March 2020 - 07:56 AM

As explained above, the exit pupil can be easily calculated by dividing the eyepiece focal length by the telescope focal ratio.   A 21mm Ethos will give the same exit pupil in any f/5 scope no matter the aperture and it will give a different exit pupil in any scope with a different focal ratio.

The only thing about this is that EP FL and FR of telescope is not an exact science.

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Posted 26 March 2020 - 08:09 AM

How do you measure the exit pupils of eyepieces to come up with exactly 4.2mm? What kind of a caliper are you using?  How can the naked eye see something that small? IMO, you need to use a digital caliper and a loupe to see that, especially when using really short FL eyepieces.

I assume TS meant the website Astronomy Tools or some other calculation tool, not measurements at the eyepiece.

The only thing about this is that EP FL and FR of telescope is not an exact science.

Can you explain your point of view? IMHO it's a perfect example of the science of optics.

### #10 Jon Isaacs

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Posted 26 March 2020 - 08:28 AM

The only thing about this is that EP FL and FR of telescope is not an exact science.

For refractors and Newtonians, the focal lengths are reasonably close.  Eyepieces too.  One could establish error bounds but when one says a 5.2mm exit pupil, it might actually be 5.2mm +/- 2% but that's insignificant.. The main thing is that it's around 5mm and not 7mm and not 2.1mm.

For SCTs, the focal length and focal ratio changes so it's less precise.

Jon

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### #11 russell23

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Posted 26 March 2020 - 08:58 AM

The only thing about this is that EP FL and FR of telescope is not an exact science.

It is close enough for practical purpose but let's go with some numbers.  My 102mm f/7 APO's have a 714mm focal length.  Let's be generous and say that the focal length of the scope could vary by as much as 25mm.   And lets say we are using a 10mm eyepiece that could have sample variation as much as 0.5mm on the focal length (so 9.5mm to 10.5mm).

So using the published 10mm and f/7 gives an exit pupil of 1.43mm.

If we adopt a 25mm uncertainty in the scope focal length then the scope focal ratio could vary from 6.75 to 7.25 which means with a 10mm eyepiece the exit pupil would be 1.38 to 1.48mm

If we now also add in a hypothetical 0.5mm variation in the actual eyepiece focal length to the 25mm uncertainty in the telescope focal length then the exit pupil could vary from 1.31mm to 1.56mm.   So in my extreme example the deviation of the actual exit pupil from the value provided by eyepiece focal length/telescope focal ratio is only +/- 0.13mm.   And real optics are almost certainly more accurate than that.

I just don't think we should confuse people trying to understand their optics by suggesting the calculation is not reliable - since it is reliable to any reasonable backyard usage.

Edit to add:  Now there are some examples where rebranders mess with the eyepiece focal length to make it seem like it is a different eyepiece.  The most extreme example I have seen is an eyepiece labeled 7mm that was actually an 8mm.   Then you have one company for example that labeled their version of eyepieces with a 0.1mm difference from what the eyepiece is when branded by other companies.  Or my 4.7mm APM UFF Ethos clone is labeled 5mm.   These are small, inconsequential differences.

Edited by russell23, 26 March 2020 - 09:02 AM.

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### #12 25585

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Posted 26 March 2020 - 09:01 AM

How do you measure the exit pupils of eyepieces to come up with exactly 4.2mm? What kind of a caliper are you using?  How can the naked eye see something that small? IMO, you need to use a digital caliper and a loupe to see that, especially when using really short FL eyepieces.

It was what astronomy.tools calculated. Normally the site is right.....

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### #13 rowdy388

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Posted 26 March 2020 - 10:11 AM

I think the fact that magnification and resolution is higher in the larger scope at equal

exit pupils is often overlooked. Experienced observers just assume this but it may not

be obvious to everyone.

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### #14 Miranda2525

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Posted 26 March 2020 - 12:47 PM

I assume TS meant the website Astronomy Tools or some other calculation tool, not measurements at the eyepiece.

Can you explain your point of view? IMHO it's a perfect example of the science of optics.

????  One needs to measure the exit pupil somehow.  My point of view was meaning that telescopes and eyepieces are off a bit in measurement of FL.

For refractors and Newtonians, the focal lengths are reasonably close.  Eyepieces too.  One could establish error bounds but when one says a 5.2mm exit pupil, it might actually be 5.2mm +/- 2% but that's insignificant.. The main thing is that it's around 5mm and not 7mm and not 2.1mm.

For SCTs, the focal length and focal ratio changes so it's less precise.

Jon

But he said exactly 4.2mm. I was just wondering how he got that.

Edited by Miranda2525, 26 March 2020 - 12:48 PM.

### #15 Miranda2525

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Posted 26 March 2020 - 12:48 PM

It was what astronomy.tools calculated. Normally the site is right.....

How do you mean? If I put an EP into my telescope, The exit pupil is there and you can measure it, but it is very difficult to do accurately.

Edited by Miranda2525, 26 March 2020 - 12:49 PM.

### #16 Miranda2525

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Posted 26 March 2020 - 12:52 PM

It is close enough for practical purpose but let's go with some numbers.  My 102mm f/7 APO's have a 714mm focal length.  Let's be generous and say that the focal length of the scope could vary by as much as 25mm.   And lets say we are using a 10mm eyepiece that could have sample variation as much as 0.5mm on the focal length (so 9.5mm to 10.5mm).

So using the published 10mm and f/7 gives an exit pupil of 1.43mm.

If we adopt a 25mm uncertainty in the scope focal length then the scope focal ratio could vary from 6.75 to 7.25 which means with a 10mm eyepiece the exit pupil would be 1.38 to 1.48mm

If we now also add in a hypothetical 0.5mm variation in the actual eyepiece focal length to the 25mm uncertainty in the telescope focal length then the exit pupil could vary from 1.31mm to 1.56mm.   So in my extreme example the deviation of the actual exit pupil from the value provided by eyepiece focal length/telescope focal ratio is only +/- 0.13mm.   And real optics are almost certainly more accurate than that.

I just don't think we should confuse people trying to understand their optics by suggesting the calculation is not reliable - since it is reliable to any reasonable backyard usage.

Edit to add:  Now there are some examples where rebranders mess with the eyepiece focal length to make it seem like it is a different eyepiece.  The most extreme example I have seen is an eyepiece labeled 7mm that was actually an 8mm.   Then you have one company for example that labeled their version of eyepieces with a 0.1mm difference from what the eyepiece is when branded by other companies.  Or my 4.7mm APM UFF Ethos clone is labeled 5mm.   These are small, inconsequential differences.

I see what you mean here. It's not significant enough to be a worry.

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### #17 Jon Isaacs

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Posted 26 March 2020 - 01:08 PM

????  One needs to measure the exit pupil somehow.  My point of view was meaning that telescopes and eyepieces are off a bit in measurement of FL.

But he said exactly 4.2mm. I was just wondering how he got that.

He said 4.2 mm.

If it were a measurement rather than a calculation, the assumption is the least significant digit has the possibility of +/- one number maybe 2

The important issue in this thread is the realization for 25585 that the exit pupil only depends on the focal length of the eyepiece and the focal ratio of the telescope.  A 4 inch F/5 with a 30mm eyepiece provides a 6mm exit pupil, a 25 inch F/5 with a 30mm eyepiece provides a 6mm exit pupil.

Jon

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### #18 russell23

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Posted 26 March 2020 - 02:22 PM

I see what you mean here. It's not significant enough to be a worry.

I certainly think it is fair (and important) to point out and keep in mind that the focal lengths of eyepieces and telescopes may vary slightly from the specifications.  Certainly when we calculate an exit pupil to the hundredths place those factors may lead to slight differences. But it definitely is not enough to negate the usefulness of the equations for calculating exit pupil for typical observing concerns.

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### #19 MitchAlsup

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Posted 26 March 2020 - 08:19 PM

EP = D/M

M = FLeyescope / FLeyep

EP = D/(FLscope/FLeyep)  = FLeyep x (D /FLscope)  but D/FLscope = 1/Fratio  => EP =  FLeyep/Fratio.

If I remember correctly, this is known of as Gaussian Closure.

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### #20 ji4m

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Posted 03 April 2020 - 12:55 PM

We can all understand the math.  Can not it be recognized how counterintuitive it is to the beginner that the image appears larger (magnified) and yet the exit pupil is smaller?

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### #21 dan_h

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Posted 03 April 2020 - 02:20 PM

We can all understand the math.  Can not it be recognized how counterintuitive it is to the beginner that the image appears larger (magnified) and yet the exit pupil is smaller?

Maybe think a little differently.

Smaller focal length eyepieces make smaller exit pupils.

Bigger focal length eyepieces make bigger exit pupils

Magnification is not a consideration. As Jon stated in post #17 above,

" The important issue in this thread is the realization .... that the exit pupil only depends on the focal length of the eyepiece and the focal ratio of the telescope. "

If you want to know magnification you need to know more about the telescope in use. Hopefully, by the time a beginner is ready to think about exit pupil, they have learned that magnification is not the most important factor in observing.

dan

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### #22 25585

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Posted 04 April 2020 - 01:13 AM

However focal ratio is scope FL ÷ aperture, magnification is scope FL ÷ eyepiece FL, and exit pupil is aperture ÷ magnification. It is a puzzle for some!

### #23 Jon Isaacs

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Posted 04 April 2020 - 06:10 AM

However focal ratio is scope FL ÷ aperture, magnification is scope FL ÷ eyepiece FL, and exit pupil is aperture ÷ magnification. It is a puzzle for some!

I am not sure what you mean here.

The two equations:  Exit Pupil = Aperture/magnification and Exit Pupil = Focal Length eyepiece/focal ratio are equivalent and just different ways to state the same thing.  It's just algebra.

Jon

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