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# Thread: Time calculation when switching print size once again

1. Thanks Ralph and MichealBriggs! I think I got it now. The formula by Micheal would work for all focal lengths. Now I am going to work on my enlarger on the procedure to calculate exposure time based on column height and focal length change. I think one more thing I have to address is the neg to paper distance is the sum of neg to rear nodal point, front nodal point to paper and the distance between the two nodal points as I think most lenses do not have these two points the same.

2. Originally Posted by dancqu
Did you forget the lens to negative distance? Any
computation which does not factor in the change in
lens to negative distance will not be correct. Have
any of those interested in this subject found or
derived A formula integrating the two? Dan

As mentioned previously (http://www.apug.org/forums/showthrea...6&page=3&pp=10), d_i = focal length * (m + 1), so the (m+1) squared equation and the image distance squared equation are equivalent. Both are correct for changing print size with the same lens.

3. Originally Posted by Chan Tran
... I think one more thing I have to address is the neg to paper distance is the sum of neg to rear nodal point, front nodal point to paper and the distance between the two nodal points as I think most lenses do not have these two points the same.
As you have the lenses you can satisfy yourself of the importance or unimportance of allowing for the location of the nodal points: just use the lenses both ways round to form an image of a distant object and measure the nominal focal length from the image plane in each case.

Best,
Helen

4. Originally Posted by MichaelBriggs
As mentioned previously...
As I've mentioned two or three times previously
and your self as well as many times, the change in
the effective speed of the lens is NOT to be ignored.
By your example I see it can make a BIG difference.

For myself the matter is academic. I use an
EM-10 which, BTW, I've calibrated for use as
a densitometer. Dan

5. I agree, but I'm working on the assumption that this is taken care of by the lens manufacturer through the aperture markings. You got to rely on something.

When a lens is focused at a distance closer than infinity, the lens is at a distance greater than its focal length thus reducing its effective aperture. However, in enlarging this distance is the distance from the lens to the paper and not from the lens to the negative, because unlike in the camera where the film is the imaging medium but in enlarging the paper is and not the negative. The negative is now the subject. So only the lens to paper distance is needed.

7. What sort of illumination does your enlarger have? If condenser, do you adjust the condensers when switching lenses?

Best,
Helen

8. I use the diffusion head. Precisely the Beseler dichro 45 color computer head with the 4x5 diffusion chamber although I work with 35mm.

9. The f-number marked on the lens is for the lens positioned one focal length from the negative, which would make an infinitely large print. As you move the lens away from the negative to make a finite size print, the lens becomes slower and the effective f-number becomes larger. This is the same problem known to larger format photographers as bellows extension. In large format photography, the effect becomes significant (approx 1/3 stop or more) when the image size is 1/8 lifesize or more. Of course, this is the typical range of enlargements when making a print so the effective f-number of enlarging lenses in use is normally larger than the marked value.

If you look up the formulas for exposures compenstation for bellows extension (closeup photography) in a book about large format photography you will find the correct forumlas that have been given on this and previous threads about changing print sizes, i.e., the formula using (magnification +1) and the formula using image distance. Both formulas account for the lens being focused and not being one focal length away from the image.

The two formulas are physical/mathematically equivalent (when the same lens is used for both print sizes) since image distance = focal length * (magnification + 1). T2/T1 = (m_2+1)^2 / (m_1+1)^2 = (d_i2/f)^2 / (d_i1/f)^2 = (d_i2)^2 / (d_i1)^2.

References: Applied Photographic Optics by Sidney Ray, p. 523; Lenses in Photography By Rudolf Kinglake, p. 99; Photography with Large Format Cameras by Kodak, p. 47; View Camera Technique (5th ed.) by Leslie Stroebel, p. 182.

A further detail brought out by Sidney Ray is that the pupil magnification factor should be included in the forumula. But since most enlarging lenses are fairly symmetric, this can probably be neglected.

Another source that was offered directly for enlarging was the "Enlarging Dial" of the Kodak Darkroom Dataguide. This is a circular slide rule-type calculator that can be used to calculate changes in exposure time with print magnification. If you "reverse engineer" it, you will find that it very closely but not perfectly follows the (m+1) squared formula. The times that it gives, for cases of at least one of the magnifications being small, are far off the purported magnification squared formula.

10. I thought dancqu was talking about the pupil magnification factor. He must not have been. I have always ignored it to keep things simple and still practical.

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