Printing question regarding exposure times

[Erik Larsen]

Hi folks, forgive my ignorance with this question.
I've been practicing getting a nice print in an 8x10 size. I have all the exposure times and dodge and burn times optimized to my liking. I want to print this negative at 16x20 and 20x24. My question is... What exposure adjustments do I need to make when going up in size from my base 8x10 exposure figures? Is there a simple calculation or do I have to burn a few large sheets and start from scratch. I seem to remember reading about a formula, but I can't locate or remember where I saw it.
Thanks for any help you can give
Erik

[Colin Robertson]

Erik, going from 8x10 to 16x20 is easy- it's a LINEAR magnification of X2, giving an increase in AREA of X4 (imagine laying out 4 sheets of 8x10 paper to make a sqare. It would be make one big 16x20). So, your exposure should increase by exactly two stops.
(Either open lens two stops, OR open up one stop and double the time, OR same aperture and quadruple the time)
From 8x10 to 20x24 is only slightly harder. Area of 20x24 = 480 square inches. Area of 8x10 = 80. So, increas is 6 times (240 divided by 80) which needs two and a half stops extra exposure.
Good luck.

[Robert A. Zeichner]

Colin's advice is correct, but you may discover that after making the larger print, you might like to make some minor adjustments. When the image is magnified more, detail may be revealed in areas that were too small to pay much attention to in the smaller size. This might cause you to want to change either contrast grade or exposure by some small amount to compensate. If economy of materials is of concern (and who among us can afford to toss 16x20 mistakes?), I would suggest making some small test prints at the larger magnification using some 4x5 sheets placed in strategic areas like ones where shadow or highlight detail might be critical. I typically use a little 5x7 / 4x5 single size easel and lay it down on the larger 16x20 easel to make such tests. Let us know what your results were.

[Erik Larsen]

Thanks guys! I was hoping it was an easy calculation. I'm so cheap, the thought of making test prints on 20x24 paper to come up with the right look was starting to get to me. I'm such a bonehead, I never considered using small sheets at a larger magnification to test results. Much to learn:)
Thanks again for the help!

[Brian Ellis]

Thanks guys! I was hoping it was an easy calculation. I'm so cheap, the thought of making test prints on 20x24 paper to come up with the right look was starting to get to me. I'm such a bonehead, I never considered using small sheets at a larger magnification to test results. Much to learn:)
Thanks again for the help!

Actually it isn't an easy calculation when the change in the print size is anything other than an exact doubling (or halving) of the original print size (as it is when going from a print on 8x10 paper to the same print on 16x20 paper, for example). With any other change (e.g. going from a print on 8x10 paper to a print on 5x7, 11x14, or 20x24 paper) you aren't changing the distance of the light source to the paper by an even multiple of 2, which makes application of the inverse square law more complicated.

The inverse square law is the one that all us non-math types hate but it says that the intensity of light falling on an object (the paper in this case) is inversely proportional to the square of the distance from light source to surface. So if the distance is exactly doubled, as in going from a print on 8x10 paper to the same print on 16x20 paper, the intensity of the light decreases by a fourth and it's easy enough to calculate that the new exposure time will therefore need to be four times the old. But if the distance isn't an exact doubling (or halving), as when going say from 8x10 paper to 11x14, 20x24, etc. the calculation of the change in exposure time becomes more complicated. The size of the light source is also relevant to all this but that gets too complicated for me.

Another factor to consider is the enlarger design. With some enlargers, such as the Beseler MX series, the column along which the enlarger head travels isn't perpendicular to the baseboard/easel/paper. The MX column is tilted forward at an angle of maybe 15 or so degrees to the baseboard. So a change in inches that the head travels along the column doesn't correspond to the change in actual distance of the head from the baseboard/easel/paper.

Daryll Nicholas used to publish a chart that provided magnification factors at every possible distance of head to paper in increments of an inch with various different enlargers including the Beseler MX series. I used that chart, in combination with the wheel that's contained in Kodak's "Basic Darkroom Guide" book, to calculate the change in exposure times when changing print sizes. That wheel is very useful once you know the change in mag factors. That change can be determined either from a chart like the one I had (I doubt that Nicholas still makes it, he's become a digital guru) or by using a ruler to measure the change in distance from head to baseboard/easel/paper and then doing the mag factor calculation.

[CG]

You may find that a 4x change in time to get a 16x20 doesn't perfectly match what you had at 8x10.

The lens extension is shorter when making a bigger print, assuming the same lens gets used - in effect you are seeing a slightly wider angle so you are "looking" at a wider portion of your enlarger's illumination. This would tend to slightly shorten the exposure.

You will probably employ a longer exposure, rather than a brighter exposure with lens more open. Reciprocity effects may push towards a yet longer exposure and minor change of contrast.

Probably the larger paper may have originated from a different batch of emulsion...maybe a slight difference there?

Regardless, 4x will be close enough to get you close, and the rest is fine tuning.

Best,

C

[Doremus Scudder]

Erik,

The calculation is not too complicated. The one I use does not take into account the change in bellows extension when changing sizes, but I find it is accurate enough. Some fine tuning is always necessary simply due to the different paper batch and the different effect a larger (or smaller) print has.

At any rate, here is the formula, based on linear measurement of one side of the actual image:

To * (Ln/Lo)^2 = Tn (Note: "^2" means "squared")

Where: To is the original time

Ln is the new length

Lo is the original length

Tn is the new time (at the same f-stop of course).

I prefer to change the time and not the f-stop unless the times are really long. Then I simply open up a stop and cut the time in half.

It is easy to make an Excel table to do the calculations for you. Just use the above formula in a cell designated To, substituting the cell names you have designated Ln, Lo, and To for the other factors in the calculation. You can then simply enter values and hit enter :-) My calculation string looks like this: ((C5/B5)*(C5/B5))*A5 . A5 is the To cell, B5 is the Lo cell and C5 is the Ln cell. The string, of course, goes in the Tn cell.

As far as dodging and burning go, simply figure them as a percentage of your basic exposure. You can then scale them up or down by calculating them with your new exposure time. For example, if a dodge is 10% of a basic exposure of 20 seconds, and your new exposure is 36 seconds, you simply make your dodge 3 1/2 seconds for the new print instead of two seconds for the old.

Don't expect to get a fine print the first try. As mentioned above, there will be some adjustments necessary.

Best,

Doremus Scudder

[Ole Tjugen]

The simple way to do this is to invest in an Ilford EM-10 enlarging lightmeter.

Take a reading in the first position, change the size, then adjust the aperture to give exactly the same reading at the same point. That should give you the same exposure time (with the same paper from the same emulsion batch).

[Don Wallace]

I don't know why (I am still a novice printer) but the inverse square doesn't seem to work for me. It is possible that I screwed up the calculations, but I have had more luck using the method outlined in an old Kodak darkroom guide with a calculator wheel. You measure the distance between two points in the negative and compare it to two points in the current print. That is the current magnification. You then measure the distance betweent the same two points on the new print size you want. You dial in the current magnification on the handy little wheel and you can then tell the time for the new magnification.

Now, I KNOW someone is going to tell me that the little Kodak wheel simply uses the inverse square method. In any case, I bought an EM-10. :D

[photographs42]

First, applying the “formula” only gets you close. If you are printing in the same work session it is closer, but if it’s a week or a year later, the variables are almost infinite. In time, with experience, you will become good at estimating exposure time by looking at the projected image.

One thing that hasn’t been mentioned is edge burning. Light falloff at the outer limits of the image is proportionally greater at larger sizes, plus, because of the larger size, it becomes more obvious. In other words, you might not think you need edge burning with 8x10 but at 16x20 it will be more pronounced.

Finally, remember that a large part of the art of photography takes place in the darkroom. Applying the formula may or may not make it “feel” right. In my experience this is particularly true in the highlight areas. After I get very close, I sometimes spend considerable time fine-tuning the highlights.

Jerome

[Leonard Evens]

Thre rationale for Doremus's approach is that if you change both the linear dimensions of the print by the same factor, then you will change the area by the square of that factor. If by so doing you spread the same amount of light over the larger area, you reduce the illumination by the ratio of the areas, and you have to adjust appropriately. But this assumes it is the same amount of light. Unfortunately, that might not be the case. It depends on the kind of enlarger you have. According to my Focal Press's edition of "Enlarging" by Jacobson and Mannheim, the rule works for diffusion illumination, but it doesn't for other light sources, such as semi diffuse or condenser. The difference can be significant.

Ole's method avoids having to worry about such subtleties. If you don't have an enlarging meter, you will have to make test prints. But you don't have to do it every time you make a print. Once you get it right for one negative, say of a step wedge, so that the resulting prints at different sizes look equally lit, you can record the ratio of the appropriate exposure times (at the same f-stop). If you do this for a selection of different sizes, you can interpolate for intermediate sizes, and get close enough. If you know the proper ratio, you just multiply the exposure time by that for aany other negative.

[Erik Larsen]

To all who took the time to help me out thank you very much! Although my head is still spinnig:) I've learned a great deal which will undoubtedly save me many failed attempts or at least lessen the learning curve. Thanks again!
Erik

[neil poulsen]

Thanks guys! I was hoping it was an easy calculation. I'm so cheap, the thought of making test prints on 20x24 paper to come up with the right look was starting to get to me. I'm such a bonehead, I never considered using small sheets at a larger magnification to test results. Much to learn:)
Thanks again for the help!

You can alway set the enlarger to the height needed for the larger print, but still print a representative segment of the larger print to 8x10 paper until it's close or right on. Then, swap for the larger print on one exposure.

[Nigel Smith]

couple of things...

I use Doremus's calc (using a PDA) and it gets me close. I do find that if the new print size is a lot different from the original then a contrast change may be required. Going up to a larger print regularly requires a harder grade paper to 'look right'.

Ole's suggestion of an EM10 doesn't work for me... they depend on changing the aperture. Firstly I like to print at a set aperture for each lens, both for using the sweet spot of the lens and for repeatability as setting it on a clickstop is repeatable. Pity they don't make a time based version!

Cheers, Nige

[Chuck Pere]

You may want to do your smaller prints using pieces cut from the large size paper. That would eliminate any box to box paper changes.

[Leonard Evens]

couple of things...

I use Doremus's calc (using a PDA) and it gets me close. I do find that if the new print size is a lot different from the original then a contrast change may be required. Going up to a larger print regularly requires a harder grade paper to 'look right'.


As I pointed out above, whether or not that method works depends on the enlarger light source.



Ole's suggestion of an EM10 doesn't work for me... they depend on changing the aperture. Firstly I like to print at a set aperture for each lens, both for using the sweet spot of the lens and for repeatability as setting it on a clickstop is repeatable. Pity they don't make a time based version!

Cheers, Nige

The following is for the more technical minded!

In principle, the scale on the enlarging meter, if it has one, should indicate a one stop difference by a change of log(2) ~ 0.3. In any case, you can measure the change in light intensity resulting from a change of one stop. Let's call it ONE-STOP. Measure the actual change when you change print size keeping the aperture constant and divide that by the quantity ONE-STOP. That is the "number" of doublings of time necessary to compensate for the change in light intensity. For example suppose ONE_STOP = 0.3 and you measure a decrease of 0.6 when going to the larger print. 0.6/0.3 = 2, so that means you needed to change by two stops. This is equivalent to multiplying the time by 2 x 2 = 2^2 = 4. Of course, you would seldom find that the decrease in light intensity would result in an integer ratio such as above. In general you would have to use a scientific calculator to raise 2 to the ratio. The exponentiation key is usually denoted by something like an x with a y superscript, and how you use it depends on the calculator. For example, suppose the decrease in intensity were 0.45. Then 0.45/0.3 = 1.5. According to my calculator 2^1.5 (2 to the power 1.5) is about 2.83. So you would multiply the time by that amount.

[photographs42]

As I pointed out above, whether or not that method works depends on the enlarger light source.



The following is for the more technical minded!

In principle, the scale on the enlarging meter, if it has one, should indicate a one stop difference by a change of log(2) ~ 0.3. In any case, you can measure the change in light intensity resulting from a change of one stop. Let's call it ONE-STOP. Measure the actual change when you change print size keeping the aperture constant and divide that by the quantity ONE-STOP. That is the "number" of doublings of time necessary to compensate for the change in light intensity. For example suppose ONE_STOP = 0.3 and you measure a decrease of 0.6 when going to the larger print. 0.6/0.3 = 2, so that means you needed to change by two stops. This is equivalent to multiplying the time by 2 x 2 = 2^2 = 4. Of course, you would seldom find that the decrease in light intensity would result in an integer ratio such as above. In general you would have to use a scientific calculator to raise 2 to the ratio. The exponentiation key is usually denoted by something like an x with a y superscript, and how you use it depends on the calculator. For example, suppose the decrease in intensity were 0.45. Then 0.45/0.3 = 1.5. According to my calculator 2^1.5 (2 to the power 1.5) is about 2.83. So you would multiply the time by that amount.

WOW! That makes my head hurt and I am one of those "technically minded" guys. And the problem with doing it by the numbers or with an EM10 is that it still only gets you close as has been pointed out by several people here.

With a little experience, you can look at the projected image, judge its brightness, and set an exposure time within a few seconds of the correct time. Usually I make a 4x4 test strip exposure of an important area of the image with two to four (based on estimated time) second intervals two or three steps either side of my educated guess exposure and it is rare that one of those strips isn’t within a second or two of what I want.

I know you can’t make that judgment until you’ve developed a feel for it, but you aren’t going to develop a feel for it if you rely on other methods. I’m all for using whatever method works for you but it seams to me that doing the math or using a measuring instrument is taking a simple task and making it complicated, but that’s just my opinion.

I have an EM10, by the way, and I haven’t used it for 20 years or so. One problem with it is that you have to measure the exact same spot on the image each time or the information is pretty useless. You may or may not have an area of solid tone to do that in every image.

Jerome

[fhovie]

Cool! - this works for me -
There is ALWAYS a test strip - rocket science is not that good on paper
Go up a size - open a stop and test
Go down a size - close a stop and test

Now - here is the real trick that I learned the hard way:
To go from 8x10 to 30x40 - keep your 8x10 on hand and take another sheet of 8x10 (of the same paper used for the 30x40) and pick a good representative spot on the 30x40 where there are a variety of tones. Make the test print (8x10 section of the 30x40) Compare your new enlargement densities to the original 8x10 and when they match - the 30x40 will have the same look as the original 8x10. At about $10 a copy - the 30x40 needs to be right the first time.