Limit Imposed by the Bellows When Making a Small Print
As pointed out, some enlargers can be fitted with recessed boards to allow placing the lens close enough to the negative to achieve focus on machines that otherwise couldnt get the lens close enough.
Good examples are some models by Durst, Beseler, DeVere, Elwood, and some Omega models. Other enlargers cant use recessed boards due to the small cross section of the bellows that taper down to a lens receiver just big enough for the lens and its mount.
You can measure the maximum bellows extension your enlarger allows and calculate the magnification m youll use determined by the negative and print size wanted to determine what focal lengths will give you what you need and still fit the enlarger.
You mentioned the use of 6 x 7cm negatives and possibly wanting 2 x 4 prints. That provides an example to see how it works.
Suppose that with your bellows fully extended the distance from the negative to the approximate position of the diaphragm of a typical enlarging lens is 135mm. Thats the limit imposed by your bellows if you cant use a recessed board. You need to project the image of the negative big enough to fully cover the 4 length of the print to make a borderless print. Suppose that the 70mm dimension of the negative must be projected to 4.3 = 109mm.
Then m = print dimension/corresponding negative dimension = 109/70 = 1.6
The lenses that fully cover the 6 x 7cm negative at all conventional print sizes are: 60mm (e.g. Rodagon WA), 80mm, 90mm, and longer.
The distance from negative to diaphragm is
p = (1 + m)f/m
The distance from the diaphragm to the print is
i = pf/(p-f)
for a 60mm WA lens p = (1 + 1.6)*60mm/1.6 = 97.5mm diaphragm to print
and i = 97.5*60/(97.5 60) = 156mm negative to diaphragm.
In the form: focal length/negative-to-diaphragm/diaphragm-to-print, we have
60/97.5/156
80/130/208
90/146/235
But 146mm exceeds the 135mm limit we measured, so a 90mm lens is too long for this enlarger.
These are not necessarily exact, but the calculated values give us approximations that are close enough for most practical purposes.