


Relation between exposure times for different sizes
Is it possible to find a correlation that allows one to calculate the exposure time for a differentsized print?
Say I print a real nice 4x5 proof print. Everything is fine, exposure, contrast, etc, but I decide to make an 8x10 of it. Is it possible to find a correlation that will work for all images or is it too chaotic with reciprocity, subjective judgement of contrast and exposure between different sizes, and other factors?
My first instinct would be to calculate the difference in area between the two prints and adjust the aperture and time to have the same total illumination density but that might not actually work.

Light expands as the square relative to the distance. Therefore, twice the height => four times as long and half the height => one quarter the time.
Steve
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simple. Keep a cloth tape measure to hand. If old lens to easel distance was 50cm and now it is 70cm, then:
(70 squared) divided by (50 squared) X old exposure time. if old exposure time was 10 seconds, it will now be 19.6
Using the area method is daft as you might adjust the cropping when you change the height. I use the above and it is dead simple. It can be that I reduce the factor ever so slightly at times to account for the bulb getting hotter in longer vs very short exposures, so instead of going from a 5 second (for a very small print) to 25 seconds for a much larger one, I might try 22 or so. I often stop down more for small prints so that I can then keep the time broadly similar by opening up a stop or half more for a larger one. with small prints you are not likely to have an issue with diffraction esp when the neg is big.

The above equations are correct, but it must be mentioned that the papertolens distance must be used (to be precise, it is the distance from the paper to the front nodal point of the lens). Some use the papertonegative distance, which returns wrong results.
As an alternative to the lenstoeasel distance, you can also work with the negative magnification. This method is very precise and often easier to measure. You can determine the actual negative magnification by having two notches in the negative carrier (I added mine with a file), exactly one inch apart, and measuring the distance between the notches on the baseboard. When changing the magnification from m1 to m2, the new exposure time (t2) is calculates as:
t2 = ((m2+1)^2/(m1+1)^2)*t1

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I appreciate the math but I use a color analyzer. My Jobo 5000 works well for this. I put one of the channels in "integrated" mode so that a diffuser is placed over the lens and over the light sensor. I place the light sensor in the middle of the print, place a diffuser under the enlarging lens, and click "measure." This will give me a log density value. Then I recompose the print at the desired magnification and repeat the process. This time the log density value is different so I gradually open the lens diaphragm until the density values are the same. That way I keep the same exposure time and all of the doge/burn sequences are the same also. However, the larger print often needs a hair more contrast because of flare, etc. Therefore I do one test print of an important area of the larger print from which I can tweak the contrast before exposing the final, larger print.
Might sound complicated but it works well. If I have a detailed printing sequence dialed into my RH Designs Stopclock timer for an 8x10 print and then decide to do a 16x20, I can figure out the new aperture easily and retain the same exposure sequence. I suppose you could do the same thing with any enlarging meter.

Measuring always has been a viable alternative to fundamental science as long as the technology is available to support it. On the other hand, solid optical mathematics does not suffer the disadvantages of electronic limitations and accuracy ranges. That said, a good measurement includes external 'noises' hard to include into a mathematical model.
In short, calculate or measure, do whatever is simpler or cheaper for you. You might have to adjust both results for different reasons.

