Maximum Size Enlargement Possible

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I'd like to know the formula for calculating the largest enlargement possible based on the maximum enlarger head height and enlarging lens focal length.

Thanks,

Dick

-- Dick Drake (dickk9ewt@earthlink.net), August 10, 2001

Answers

LOL.....Dick, bubba! What enlarging lens are you using? how high is your enlarger column? what format are you using? theorethically I can make an infinite size print if I have a source of light strong enough, and a lens big enough and a column tall enough! The size and image quality will depend on the format you are trying to enlarge, the lens you are using and the height of your column, without that information is hard to help you. Also remember that quality is an issue, if you are enlarging 35 mm, then a 10x magnification is about the most I would do, now if you have a 4x5 neg you can do 20x or 30x with reasonable results....

-- Jorge Gasteazoro (jorgegm@worldnet.att.net), August 10, 2001.

Dick, most manufacturers have charts which has this information: format, lens and max size. Check out the enlarger manufacturers web site.

-- Jeff White (jeff@jeffsphotos.com), August 10, 2001.

I have a 23cII enlarger, standard column, which I want to use for 6x7 in addition to 35mm. I have seen a formula to calculate max print size based on lens focal length and enlarger height. However, I haven't been able to find it searching via Google. I'll check the manufactures web sites.

Thanks, Dick

-- Dick Drake (dickk9ewt@earthlink.net), August 10, 2001.


If you already have one enlarging lens, you can determine the maximum magnification level of your enlarger (using normal focal length enlarger lenses). Then you can apply the same magnification level to the other lens. This will work fairly well in comparing 50mm (for 35mm) and 80mm (for 6x7). If you want to use a 105mm for 6x7 there are some extra calculations that need be performed. Please tell us what you can achieve (largest print size) with your existing lens (assuming you have one). And please provide detailed information about the existing lens (including manufacturer).

-- Michael Feldman (mfeldman@qwest.net), August 10, 2001.

Using a 50mm Nikor lens,a 35mm negative and the enlarger fully raised (30 3/4" above the easel to bottom of the lens), the largest print size is 13"x18".

I want to be able to get 11x14 prints from a 6x7 negative. I'm thinking that I would need a wide angle lens.

Dick

-- Dick Drake (dickk9ewt@earthlink.net), August 10, 2001.



You asked for the formula in terms of enlarger head height. This is the most useful form, but a bit more complicated than those using just the negative-to-lens or lens-to-paper distance. The Focal Encyclopedia almost gives it, but doesn't break it down into the form you want, so here's my effort at it. I've verified this by measurement, but someone better with math can probably simplify it a bit. Note that it uses the thin lens formulas, but is accurate enough for most purposes. The form is similar to the quadradic formula you learned in high school. M=(((D/F)-2) plus or minus the square root of ((D/F)-2)^2 -4)/2, where M is the magnification, D is the distance from the paper to the negative carrier, and F is the focal length of the lens. Keep the units the same and note that everything gets divided by that last "2". Say you have a 2" lens (50mm) and the neg to paper distance is 24". M, the magnification will work out to 9.899X. From that you can get the max print size. You can use any negative dimension, but if you use the diagonal of a 35mm frame (1.7"), the largest uncropped print will have a diagonal of 16.828". Hope this was more useful than some of the earliest replies :-)

-- Conrad Hoffman (choffman@rpa.net), August 10, 2001.

Since the 35mm frame is about 1.5" long and the largest print size you are getting is 18" using the "normal" 35mm lens (50mm), then you are achieving a magnification level of about 12x. Since the 6x7 negative is 2.75" long, you can achieve approximately a maximum print size of about 33" (12*2.75) using a normal lens for 6x7 (80mm f/5.6 El-Nikkor for example). If you use a 105mm lens for the 6x7, you can achieve a maximum print size of 25.1" (80/105*33). These calculations may not be exact, but should be close enough for your purposes.

Next time someone asks for all the details about your lens (do you have the 50mm f/2.8 or the 50mm f/4?) please provide everything. It is usually better to provide too much info than not enough.

-- Michael Feldman (mfeldman@qwest.net), August 11, 2001.


Opps! I forget to apply the final calculation. Need to adjust for the differece between the 50mm and 80mm lenses. Therefore, the maximum print size would be 33*50/80 = 20.6". In reality, the maximum print sizes should be about the same if you use the normal lens for each format (50mm for 35mm negs and 80mm for 6x7). My apologies.

-- Michael Feldman (mfeldman@qwest.net), August 11, 2001.

Divide the Distance from the negative to the baseboard by the focal length of the lens. (Be sure to use the same (inches or mm) for both). This gives you the magnification ratio for large prints. Example: negative height 24", focal length 2", 24/2=12. For a 35mm negative which is about 1" x 1.5", the print size is 1*12 x 1.5*12= 12"x18".

-- Bill Mitchell (bmitch@home.com), August 11, 2001.

Dick;

Since my wet darkroom is next to my digital, I measured both lens.

a 13x19 inch size with a 35mm carier and 50mm f 4 el-nikkor, is 17 3/4" x 21 1/2" with a 80mm el-nikkor and 6x7 carrier.

-- Gene Crumpler (nikonguy@att.net), August 11, 2001.



Thanks to all who responded.

Dick

-- Dick Drake (dickk9ewt@earthlink.net), August 11, 2001.


I think Conrad got the equation correct. The equation can be simplified a bit further. If L is the distance from the easel surface to the negative and f is the focal length of the lens, define R = L / f. Be sure to measure both L and f in the same units, e.g., mm.

The equation becomes: m = R/2 - 1 +/- sqrt (R*R/4 - R).

In words: R divided by 2, minus 1, plus or minus the square root of the quantity (R-squared divided by 4, minus R).

For the case that the image is magnified (m > 1), take the plus sign. This is the case that the original question wants. The negative sign will give m < 1, the value being the reciprocal of the plus sign case.

-- Michael Briggs (MichaelBriggs@EarthLink.net), August 12, 2001.


Geez! What's all this square root business?
All that's needed is to divide the maximum distance between the negative carrier and the baseboard by the focal length of the lens. That gives you M+1, as near as dammit, where M is the maximum magnification of enlargement you can make. With a 90mm lens and over 30 inches of throw, you can get a 7 times enlargement easily. That means a 16 x 18 inch print is possible.
If you go to a 105mm lens, then you can still get a 6 times enlargement, or a 15" x 13" print from 6x7cm.

-- Pete Andrews (p.l.andrews@bham.ac.uk), August 14, 2001.

Pete, the root term becomes important with longer lenses, say with a 5x4 enlarger and 135mm lens. I admit that for a 35mm neg and 50mm lens, the approximations are plenty good enough. I think your formula gives M+2 though. Just for fun, try the 1:1 magnification case with both formulas, say a neg to film distance of 400mm and a focal length of 100mm.

-- Conrad Hoffman (choffman@rpa.net), August 15, 2001.

The total distance from subject plane to image plane is actually given by f x (M+1 + 1/M). Still no sqare root function you'll notice!
The term 1/M gets more significant as the magnification reduces, but for most rough 'n' ready purposes where M is much greater than 1 it can be ignored, or at least approximated. My 'guesstimates' are out by about 1/7th and 1/6th respectively, but then the 30" measurement given was from the lens to the baseboard. So sue me for the difference.

-- Pete Andrews (p.l.andrews@bham.ac.uk), August 17, 2001.


Naw, at best the judge would only award a couple millimeters, and we'd have to give at least half of that to pay the barrister :-)

-- Conrad Hoffman (choffman@rpa.net), August 17, 2001.

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