Another way of determining the focal length

[T3D john bercovitz <bercov@xxxxxxxxxxx>]

I haven't done an error analysis on this method.  It relies on
using the focussing glass twice so there is some question of
course but my test with ground glass found I was at least very
consistent using it (see earlier post).  This method works
regardless of the length or sense of the hiatus but it will be
confounded if you have elements that move independently from the
main body of the lens during focussing (floating elements).

1) Check infinity focus.  Measure position of lens.

2) Focus on some nearby object.  Measure position of lens.

3) Measure size of object and size of image to get magnification.
   Call magnification "m".

4) Calculate movement of lens from 1) to 2).  Call this distance
   "delta s'" or "ds'" for short.

fl = focal length
s = distance to object from lens
s' = distance to image from lens

s1' + ds' = s2'

s2'/s2 = m

Starting with the familiar general equation:

1/s2' + 1/s2 = 1/fl

1/s2' + m/s2' = 1/fl

1/(fl + ds') + m/(fl + ds') = 1/fl

Solving for fl:

fl = ds'/m

Now let's plug and crank some real values.  Taking a 55 mm micro
nikkor, I measure the lens motion from infinity to all the way out
to be 27.9 mm +/- 0.2%.  I move the camera back and forth relative
to a grid until the grid is in focus (with the lens still racked
all the way out).  I shoot the picture.  I measure the negative
and find the magnification was 0.51 +/- 1% (there's the killer).
So:

fl = ds'/m = 27.9/0.51 = 54.7 mm +/- 1.2%

Oh well, good enough for a rough check, I guess.  8-(  Better to
get closer to the heart of what you want by measuring using John
Ohrt's methods or just shoot the same grid from the same distance
with two different lenses and compare the magnifications.

John B

PS: I guess it would have helped if I'd said s1' = fl but y'all
folks knew that, right?  Because if s = infinity, then s' = fl.


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End of TECH-3D Digest 150
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