I hope someone's answer to questions #1 and #2 in boldface below will help me to choose great perspective for portraits in 4x5 and 8x10. I want a careful answer that I can understand, so I introduce some math. The quiz is supposed to be a fun way to introduce my questions , and I think it can help us avoid the pointless arguments and inadequate rules of thumb that usually dominate this kind of subject.
To keep things simple, assume no movements (and no rise, fall, or shift). The lens is rectilinear, and possibly a telephoto.
Recall from photography kindergarten that when we focus a particular lens, that determines the distance from the lens to the plane of sharp focus and the magnification achieved there. Furthermore, any line segment centered in the plane of sharp focus is imaged as a line segment centered in the film plane, and the line segment in the plane of sharp focus determines an angle from the front nodal point. Here are some variables we can measure:
f = lens focal length;
u = distance from the front nodal point to the plane of sharp focus;
v = distance from the rear nodal point to the film plane corresponding to u;
m = image magnification;
s = length of a line segment centered in the plane of sharpest focus (in the subject);
z = length of the line segment centered in the film plane corresponding to s;
a = angle that the line segment of length s forms from the front nodal point.
What I said about photography kindergarten can be restated in terms of these seven variables. That is, if we know f, u, and z, then we can deduce v, m, s, and a---provided the data is logical and consistent.
In this post, assume that the numbers we are given are logical and internally consistent, meaning, for example, that we never have a situation that assumes or implies u < f or v < f. Another way to say this is that the data we are given is measured with perfect accuracy. We may as well assume that f, u, v, s, and z are all measured in mm. And to sidestep a few unnecessary complications, assume that all of the numbers are positive and finite: In particular, we are not focusing at infinity.
It looks like there must be four equations relating my seven variables, because assigning three values determines the other four. We have seven equations in seven unknowns. The seven equations here are three variable assignments (f, u, and z) plus four other equations needed to deduce v, m, s, and a.
Quiz problem A: Write out four equations that allow us to determine v, m, s, and a from known values of f, u, and z.
Quiz problem B (optional): Of the seven variables I listed above, some combinations of three variables suffice to deduce the other four. But some do not: For examle, f, u, and v determine m, but not z, s, or a. List all of the combinations of three variables for which the values of the remaining four variables can be uniquely determined. We already know that (f, u, z) is yes, but (f, u, v) is no. There are 35 possible combinations of three variables (7 choose 3 equals 35), so the question is which of these 35 combinations of three allow deducing the other four variables?
Question #1: What distance to the subject determines the perspective with a print of a three-dimensional subject that fills the frame? I am guessing that the subject-to-film-plane distance is only an approximation, and that the exactly correct distance that defines this perspective is the subject-to-front-nodal-point distance.
I should be more specific. Suppose my 8x10 portrait print was shot with a particular lens on 35mm film. It is an enlargement from a 24 mm by 30 mm area on the film. And suppose that I want to match that perspective with large-format film. My question becomes this: What distance should I hold constant to duplicate that perspective with an 8x10 camera? (This will define what focal length we should use.)
I think the answer is to keep the subject-to-front-nodal-point distance the same between formats, but I am not sure. Keeping this distance constant as I vary formats, it seems to me, will keep the relative positions and sizes of the nose and ears unchanged in the images. It will also keep visible precisely what was visible before. Can anyone say for sure, or maybe even offer some proof?
My next question makes sense only if my guess for the answer to question #1 is correct.
Question #2: I want great perspective for head-and-shoulders portraits. In the world of 35mm, a 50 mm lens for this kind of portrait is considered terrible---too short. An 85 mm lens is okay, but many pros prefer 300 mm. In summary, some 35mm pros say that 50 mm is terrible, 85 mm is okay, and 300 mm is great (for shooting a head-and-shoulders portrait).
Still assuming that my guess for question #1 is correct, you can see that the 35mm pro advice for great head-and-shoulders portraits can be restated as advice on the proper subject-to-front-nodal-point distance.
Using your answers to quiz problem A or B, you will see that their counsel is that for head-and-shoulders portraits, a subject-to-front-nodal-point distance of 2.4 feet is terrible, 4 feet is okay, and 14 feet is great. To arrive at these distances, I assumed that 16 inches in the plane of sharp focus corresponds to 30mm in the film plane, i.e. z = 30 and s = 16*25.4 (because 25.4 mm = 1 inch).
In 8x10, matching these three subject-to-front-nodal-point distances require focal lenghts of approximately 280 mm, 480 mm, and 1680 mm. (I used z = 10*25.4 and the three I values computed above.) Using our hypothetical 35mm pro's appraisals, this means that 280 mm is terrible, 480 mm is okay, and 1680 mm is great.
I think modern 8x10 portrait shooters ignore this advice. So here is my question: Shooting portraits with 8x10 film, are we, without good reason, accepting generally poor and unflattering perspective?
Few 4x5 portrait shooters heed the 35mm pro's advice either, for it becomes this: 180 mm is terrible, 300 mm is okay, and 1040 mm is great.
Does anybody shoot 4x5 portraits with lenses anywhere near the recommended 1000 mm? Does anybody shoot 8x10 portraits with lenses anywhere near the recommended 1600 mm?