Barlow placement and magnification calc.

As I understand, the power of a barlow changes with the distance from the eyepiece. How does one calculate the power when the barlow is placed in front of a diagonal?

You need to know Barlow lens' focal length, which is given by f=i/(1-1/M), where "i" is the lens-to-original focus distance when Barlow is in position in which refocuses magnified image to its top opening (where the ep field stop is supposed to be). The inside focus distance "i" is approx. given by L/M ("L" being lens-to-top of a Barlow separation, and "M" its designated magnification).

Once you know "f", magnification of a Barlow for any lens-to-ep-field stop separation "s" is given with a simple (thanks to Mike Hosea) formula M=1+s/f.

For instance, a "shorty" 2x barlow about 60mm long would have the lens inside-focus distance i~60/2=30mm. This would give f~30/(1-1/2)~60mm. With 1.25" diagonal extending the lens-field stop separation by about 60mm, for a total separation of about 120mm, new magnification needed to have image refocused to the ep field stop is M~1+120/60~3.

Note that this is applicable only to reguler Barlows, with a single lens, or lens group.