There have been so many posts on here about Eyepieces (EP's) that I thought I would try to help clear the mystical waters of the math required for you to determine what you want and need.

First thing though, is all calculations here are going to be in Millimeters (mm). The calculation to convert inches to mm is:   25.4 X ?inches = mm.

For the purposes of this tutorial we will be using the same telescope for all calculations. The telescope is of 8" Aperture (203mm) with a focal length of 1200mm. We will be using Plossel EP's with a 52 degree Field of View (FOV).

First step in our calculations is to determine a starting point for our chosen EP line. This will require us to determine our lowest power EP Exit Pupil. The average human eye can dilate to about 6 to 7mm in the dark when fully adapted (6mm for us older folks), we will use 7 mm for our calculations. Our lowest power EP should not exceed this limit as it surpasses our eye's ability to take in all the light. It also reduces contrast and image quality is impacted. The Exit Pupil of an EP is determined by the telescopes Focal Ratio and the Focal Length of the EP. The Focal Ratio of our telescope is the Focal Length divided by it's Aperture. So 1200 / 203 = F 5.9.....We can now take our Focal Ratio and multiply it by our desired Exit Pupil of 7mm to determine our lowest power EP. So:     5.9 X 7 = 41.3mm. Our lowest power EP should be around 41mm give or take about 10%.

Now we want to determine other EP's we would like, to incrementally increase our magnifications. It has been determined that for the human eye to noticeably see an increase in magnification we must make steps of a factor of 1.4 X so we will start with our 41mm. To determine it's Magnification we will divide the telescopes Focal Length by the EP's Focal Length. 1200 / 41 = 29.25X. Now we multiply 29.25X by our factor of 1.4X or:   29.25 X 1.4 = 41X. The next EP we want in our line should give us 41 power. Now we take the next power step of 41X and divide it into the telescopes Focal Length to get the Focal Length of our next EP. So:   1200 / 41 = 29.25mm. The next EP we would want in our line should have a Focal Length of 29mm give or take again about 10%. We would continue to calculate like this until we reach our telescopes Maximum Magnification.

Maximum Magnification is easy to calculate as it is usually stated as 2 times the telescopes Aperture. In our case here we have 203mm of aperture so:    203 X 2 = 406. Our telescopes Maximum Magnification is 406X. This is stated for the reason that this telescope will not increase any detail above this limit (resolution). It is true things can be magnified more but detail will not increase, and probably will suffer due to atmospheric conditions. Most telescopes are limited to powers below the Maximum due to atmospheric conditions any way. You will find that most sky conditions limit even the largest telescopes to 300X or less. It is a rare night that you can go above 300X.

Earlier we mentioned that our Plossel EP's have an AFOV of 52 degrees. This will help us determine the EP's True Field of View (TFOV) in our telescope. This is handy when we want to frame an object in our EP, like the Moon. We know the Moon covers about 1/2 of a degree in the sky. To determine an EP's TFOV we will take an EP's given AFOV and divide it by its Magnification. Earlier we calculated that a 41mm EP with a 52 degree AFOV would give us 29.25X. We now take our EP's 52 degree AFOV and divide it by its Magnification of 29.25X. So:   52 / 29.25 = 1.77 degree. This means our 41mm EP will yield an TFOV of 1.77 degrees. A 17mm EP would give us an TFOV of 0.73 degrees.

With the above calculations you can determine a lot of things about your EP's and telescope combination. It is not too complicated to sit down and figure these things out using the formulas above. After doing it a few times you will get very used to it. There is no magic here just math. I hope this has not muddied the water any more for you than it already was. We have covered the most important things about EP's here. Good luck now with you EP calculations, and clear skies.

JJ 

Thanks JJ, that answered all of the questions that i ask myself when i 'm reading about eyepieces.,. that is.,, except,.,where will i get the $ for that !!!.,.,., O+O

JJ,

 Do you suppose you can say anything about the use of Barlows?

How they combine with certain size eyepieces, what they are useful for etc.

As of now I know they are used to increase your view by 2X. As far as what the rules are with doing this I am clueless. Thanks again. 

m0nk,

Barlows are very useful in in short focal length telescopes..(ie 750mm or less) to achieve higher magnifications. They can still be used with longer focal length telescopes too. Certain EP designs like Plossels have eye relief that gets shorter with their focal length. In the case of Plossels the eye relief is about 0.7 times its stated focal length. If you had a telescope that required a 5mm EP to reach 250X the eye relief for a 5mm would be about 3.5mm. That requires you to be very close to the EP to view and will make viewing very uncomfortable as your eye may even be touching the EP. In this case you could use a 10mm EP and a barlow to get 7mm of eye relief and maintain 250X magnification. You will also note that in the Plossel design, as the focal length decreases so does the size of the optical glass opening you view through. The Barlow allows you to use EP's with larger openings to achieve the desired magnifications. Some EP's with set eye relief for the series (ie..20mm), this will not be a factor.

Barlows also allow a person to effective double the number of EP's that you have. Lets say you have a 20mm, 17mm, and a 12mm set of EP's. Use a Barlow to get a 10mm from the 20, and 8.5mm from the 17 and 6mm from the 12. Basically you now have 6 focal length EP's from just 3. It is a cost effective way to allow for more focal lengths and maintain good eye relief.

Barlows begin to have problems with longer focal length EP's in telescopes with short focal lengths though. With EP's of say 27 to 40mm they can cause Vignetting, which is a drop off in the light around the outer edges of the field, and in these focal lengths, Barlow design begins to extend eye relief to much. They can also cause a dark area in the center of the field of some reflector telescopes due to the center obstruction. They are best and most useful with EP's of 20mm and less.

Remember, when using an EP Barlow combination, do not exceed your telescopes Magnification Limit. 

JJ 

JJ - thanks!  A very helpful post ... just in time for shopping to add a couple more EP's.

Very well done!   "Post of the Year".........................so far.

-Jim

J.J. you make it a lot easier to understand . Thank you very much .

johnjohnson:

Earlier we mentioned that our Plossel EP's have a FOV of 52 degrees. This will help us determine the EP's Apparent Field of View (AFOV) in our telescope. This is handy when we want to frame an object in our EP, like the Moon. We know the Moon covers about 1/2 of a degree in the sky. To determine an EP's AFOV we will take an EP's given FOV and divide it by its Magnification. Earlier we calculated that a 38mm EP with a 52 degree FOV would give us 31.5X. We now take our EP's 52 degree FOV and divide it by its Magnification of 31.5X. So:   52 / 31.5 = 1.65 degree. This means our 38mm EP will yield an AFOV of 1.65 degrees. A 17mm EP would give us an AFOV of 0.73 degrees.

JJ, do you have FOV and AFOV reversed?  I always thought plossls had an AFOV of 52 degrees and, for example, my FOV was (for my 26mm plossl) at 58x gave a 52/58 = 0.9 deg. FOV.  Also, I've understood FOV and TFOV (True Field of View) to be the same thing.  I don't mean to quibble, I just thought I understood it to be the other way around...

-StarNerd

StarNerd,

You are correct, but for the purposes of this post, I tried to keep it simple, and what makes the best sense to a beginner. In most catalogs that a beginners gets the EP's are described as having a certain FOV. Orion is terrible for it.  I could have described it as having an "Actual Field of View" to be a little more specific. Thanks for paying attention.

JJ 

Oh, OK!    That's some great, concise info.  As a newbie, I remember getting onto the Televue website and that was scary!  After a few months of study, I finally figured it out, and I ended up taking calipers to measure the field stops of my plossls, which was probably overkill, considering that the equations you give above yield the same results without having to use calipers.   It was a good academic exercise, however.

I tried to remove the "SCARY" and replace it with common sense. Use descriptive words and explanations that most of us simple minds can understand. I went through the all of the "Trying to understand" problems also. I have just tried to simplify it to the base. Eliminate the difficult, and deal with the real. Reduce everything to it's simplest common denominator..

I hope this thread has helped many people that were afraid to even ask the questions. I was at first. I learned the hard way. Many hundreds..No thousands of dollars..spent wrong!

If this helps just one person it was worth it!

JJ 

 Great post John, informative and helpful, and worthy of a "sticky". Thanks for posting this, and thanks to Karri for pinning it for us.

 JJ,

   Another question about barlows and focal lengths. You said they are more useful for short focal lengths. What about long focal lengths? Wouldn't a 2x barlow still be useful here? I thought they would be a cost effective way of getting different magnifications without buying 6 eyepieces regardless of focal length. I'm asking this because I was looking at a 1500 focal length f/10 scope and thought about buying a 2x televue powermate with 2 eyepieces (24mm and 11mm), rather than buying 2 more expensive eyepieces. Thanks once again for any help!

Barlows work with longer focal length eyepieces also, but the problem comes with the eye relief.  Longer focal length eyepieces have longer eye relief naturally, and the barlow extend this even further, sometimes to the point where it can be difficult to find the "sweet spot" for viewing.  It would depend on what the eye relief for the eyepieces you are consideing are, but I wouldn't anticipate a problem with a 26mm EP.

The 24mm Orion Stratus has an eye relief of 15mm. The Televue 11mm nagler has an eye relief of 12mm. The "barlow" is the Televue powermate 2'' which is supposedly a bit better than a real barlow. The telescope in question is a 152mm MCT.

  Who knew there were sweet spots involved here...

I've barlowed my 24mm Baader Hyperion (essentially the same as the Stratus) with no problem. The 11mm Nagler would do fine also.

Powermates were designed to not effect the eye relief of an eyepiece. They may be used with long focal length EP's usualy with out problems. Common 2 element barlows will extend the eye relief of low power EP's. In short focal length telescopes (F6 or less), they can begin to cause vignetting with long focal length EP's. This is a drop off in light around the outer edge. In many cases with the long focal length EP's the barrel of the EP is also the field stop. Many barlow's field stop are less than that. In effect you are stopping down the EP's field of view. If used with a reflector you may also notice a darkened area in the center of the field which is the center obstruction of the secondary.

One can try a Barlow with a long focal length EP, and you scope design, but look for the anomaly's mentioned above. If you do not see them then no problem. 

JJ 

THANK YOU SO MUCH JOHN!  While I knew enough to know the power by taking the focal length divided by the mm listed on the lens, I had not even considered AFOV.  I would have bought a 4mm lens with a 55 degree field of view not even realizing that for my scope that would translate into a .3 degree AFOV....Not very wide at all as I'd like to go no lower than half a degree.  This was very helpful for a noob like me!

What a wonderful post.  This should be required reading for noobs like me.  It probably cut the amount of questions I had in half.