Magnification & Exposure changes: A no-calculations method
Using an f-stop timer without an enlarging meter to provide exposure compensation can be easy ... if one measures distance in stops.
With the right ruler one need only measure the lens height or image size before and after the magnification change and subtract the two readings - the result is the required correction in stops.
A pdf file for such a ruler is provided at:
As an f-stop timer works in logarithms (stops being logarithms base 2) the calculation of the correction becomes simplified if the distance is also measured in stops: division turns into subtraction and squaring turns into doubling. A logarithmic ruler marked in 2*log2(distance) reads the correction factor directly.
If great accuracy is needed then an exposure meter should be used. Different enlargers require different corrections for the non-square-law light fall off from the condenser or diffuser to the lens. This correction is only critical at small magnifications where the lens-light source distance changes greatly.
The stops-ruler method can, of course, be used with other timers by using an f-stop timing dial or stops table.
Example using a a timing dial http://www.darkroomautomation.com/support/grastops.jpg:
- Measure 3.6 as the image size using the stops-ruler
- Raise the head to the new magnification and focus
- Measure 2.0 as the new image size
- Correction is 3.6 - 2.0 = 1.6 stops increase to exposure
- Gralab pointer is at 3.2 (~9 seconds): 3.2 + 1.6 = 4.8. Move pointer to 4.8 (~28 seconds)
Using a stops table http://www.darkroomautomation.com/su...stopstable.pdf:
- As above, measure original size as 3.6, new size as 2.0, difference as 1.6.
- Timer is set to 9.2 seconds - read across on table to 3.2 stops.
- 3.2 + 1.6 = 4.8. Look up time for 4.8 stops and set timer to 27.9 seconds.
More complicated than using an f-stop timer, but easier than:
- Measure old size as 9 3/4" and new size as 16 7/8"
- The rest is left as an exercise for the reader...
If you wanted that in stops to open lens, rather than using the ruler and subtracting 3.6 - 2.0 = 1.6 stops, the scientific calculator comes out and log10 ((new / old) ^ 2) / log10 (2) ...
Note the f-stop ruler's numbers decrease as the head is raised, this is because the light, in stops, is decreasing. As the light decreases by X stops the exposure time is increased by the same value to compensate.