I've often read that a regular Barlow (as opposed to a Telecentric, like a TeleVue Powermate) will increase the eye relief of any eyepiece that's used in it.
Is there any formula for figuring out how much? Is the formula different for 2-element Barlows vs. 3-element Barlows? Or is it different from shorty Barlows to long-form Barlows?
I'm wondering because I just picked up an old Orion Ultrascopic 3-element long-form Barlow (it's 5 1/2 inches long), and was wondering what to expect in terms of eye relief when I use it.
A long time ago on CloudyNights there was a post on this topic. Here's the text of what I have regarding that post:
Barlowed Eye Relief Made Easy #1957912 - 11/03/07
Years ago I derived an empirical formula for calculating Barlowed eye relief. The only problem with the formula (until now) was that it was accurate only for the 2" 2X TeleVue Big Barlow. The problem was that the "constant" in the equation was specific to only the TV Big Barlow. That has all changed, as I have since quasi-empirically derived constants for a number of Barlows, which I will present here along with the formula.
ER_Barlowed = ER_ Original + (FL/C)^2
ER_Original = the eyepieces standard (non-Barlowed) eye relief.
FL = the eyepieces focal length
C = the Barlows specific "constant" of eye relief growth (the constant)
^2 = squared
ER_Barlowed = the eyepieces Barlowed eye relief
Here are the constants (values of 'C') which I've derived for a range of Barlows for which people have been kind enough to measure them (or for which I have measured them myself):
2" 2X TeleVue Big Barlow, C = 11
1.25" 2X TeleVue Barlow, C = 10.36
1.25" 3X TeleVue Barlow, C = 10.58
1.25" 2.5X TeleVue Barlow (discontinued), C = 11.11
1.25" 2.5X TeleVue Barlow (3X top on 2X Barlow), C = 11.38
1.25" 2.8X Klee Barlow, C = 7.16
1.25" 2.2X Klee Barlow, C = 8.83
1.25" Orion Shorty Plus Barlow, C = 8.86 (assuming 2.2X for this Barlow)
1.25" Celestron Ultima Barlow, C = 8.83 (assuming 2.2x for this Barlow)
2" 2X GSO ED Barlow, C = 11.49
1.25" 2X Takahashi Barlow, C = 10.67
2" 1.5X Proxima Barlow, C = 12.33 (if in fact it is 1.5X, but I now strongly suspect it is 1.6X and identical to the Antares below it)
2" 1.6X Antares Barlow, C = 11.62
1.25" 2X Lomo Barlow, C = 8.33
1.25" 3X Vixen Barlow, C = 11.25
2" 1.7X Astro-Physics Barcon Barlow, C = 12.00
With these constants, my simple empirical formula is now fully usable with all Barlows for which some simple length measurements are known. Enjoy.