Eyepiece focal length measurement

I measure focal length using an adaptation of the method described by Don Taylor in a usenet posting in February 2000. The focal length is derived from the measured magnifications of a grating when it is projected through the eyepiece on to two screens.

I used a laser printer to print a 100 lines per inch grating onto overhead projector film. (You can download a PDF version of the postscript grating file.) This grating is attached to a slide projector with double sided tape. The eyepiece under test is carefully positioned in front of the grating, as shown in the picture, so that the grating is focussed onto screens one or two metres away.

I printed a set of projection “screens” with black bars at various pitches from 10 mm to 80 mm. These can be easily pegged to a stand and then moved about until the projected grating lines have the same pitch and line up with the printed lines. (Sliding the screen sideways so that the projected dark lines fall in between the printed dark lines is quite a sensitive test of this.) The picture shows the grating projected through a 25 mm Plössl eyepiece onto a 20 mm pitch screen at just over 2 metres distance. I simultaneously use two screens of different pitches and then measure the distance between them with a steel tape measure.

The maths to compute focal length is fairly straightforward. The advantages of using two screens at different distances are that it is not necessary to measure the (longer) distance from the screen to the grating, and there is no error introduced by the unknown distance between the principal planes of the eyepiece.

There are four numbers needed: the pitch of the grating d (0.254 mm for a 100 lines/inch grating), the pitches of the two screens D1 & D2 (e.g. 10 mm & 15 mm) and the distance between screens L.

First, compute the two magnifications:

M1 = D1 / d
M2 = D2 / d

The focal length is then:

f = L / (M2 - M1 + (1/M2) - (1/M1))

I take two measurements of L for each eyepiece to get the range of values over which I judge the screens and projected grating to be aligned. This gives some idea of the inaccuracy of my measurements.