# Thread: Portrait perspective: Quiz and two questions

1. ## Portrait perspective: Quiz and two questions

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?

2. ## Re: Portrait perspective: Quiz and two questions

Jerry,

I hope you'll forgive me for opting out of your math quiz, and consider the role of the film format in reproduction magnification and optimum viewing distances as clues to the reasons perspective rules that apply to 35mm format do not necessarily translate to larger formats. For what it's worth, my favorite portrait lens in 35mm is a 58mm f 1.2, which produces results roughly analogous to my 14 1/2" f4 Verito, which is one of my favorite portrait lenses for 8x10. Good luck with your calculations.

Jay

3. ## Re: Portrait perspective: Quiz and two questions

Dear Jerry,

"...some 35mm pros say that 50 mm is terrible, 85 mm is okay, and 300 mm is great..."

Two questions: Why all the math? What do the "other pros" say?

4. ## Re: Portrait perspective: Quiz and two questions

"(For 35mm) 50 mm is terrible, 85 mm is okay, and 300 mm is great (for shooting a head-and-shoulders portrait). "

I consider this one of those "inadequate rules of thumb that usually dominate this kind of subject". :-)

As a counterpoint, I offer the Kodak book "The Portrait", which recommends a 75mm lens in 35mm and 14 to 16 inches (355-400mm) for 8x10 head-and-shoulders portraits. Perhaps not ideal (I prefer slightly longer myself), but certainly adequate, and far from producing "generally poor and unflattering perspective".

Of the working professionals I know, there is not one who uses a 300mm as their main lens to do head-and-shoulders portraits on a regular basis. Sure, I have tried it myself, but any focal length say above 85mm is very adequate (and even much shorter, but that would require a lot more skills from the photographer). The problem with a very long focal length is that the working distance becomes terrible in communicating with the model. I consider this communication vital in getting a good expression with the subject, which in turn is what makes a good portrait. 300mm is great for candids though.

By the way, I noticed the "best" perspective are a bit further away with Caucasian than with Asian subjects, for my taste, generally speaking; it still depends on the specific subject. 90mm (in 35mm format) works reasonably well to achieve a more traditional/standard head-and-shoulder portrait with most subjects.

Cheers,

- Phong

5. ## Re: Portrait perspective: Quiz and two questions

There's an empirical, if not mathematic basis for 300 mm 4x5 portraits. The diagonal of a 35 mm negative is 43 mm; twice the diagonal is 86 mm. 85 mm is a very popular portrait lens for that format. The diagonal of a 4x5 is 150 mm; by analogy, 300 mm is the "optimum" portrait lens.

Occasionally I will use a 135 mm lens for 35 mm head shots, but I think it's a bit much for my style.

HOWEVER: this is just me; or as the younger generation would say, "YMMV." Anyone can take my advice, and a twenty dollar bill, and buy a cup of coffee at Starbucks.

Good shooting.

/s/ David

6. ## Re: Portrait perspective: Quiz and two questions

When I was a portrait photographer we used 210mm lenses on the 6x7cm format. Which equals 105mm on 35mm, 360mm on 4x5. Now I prefer 90mm on 35- but that's because it's the lens that fits the camera I like best for portraits. Plenty of people shoot portraits on 8x10 but I'd guess that few use a 600mm lens (the approximate equivalent). That may be due to the logistical and d-o-f problems with such a long lens. But it really comes down to what works- and that's most often, a slightly longer than 'normal' focal length.

7. ## Re: Portrait perspective: Quiz and two questions

"Perspective" is determined by camera to subject distance and nothing else.

As an example, any camera and any lens at five feet from a subject will produce the same perspective. Framing may change, perspective will not.

8. ## Re: Portrait perspective: Quiz and two questions

It's perhaps less applicable to formal portraits than to other photographs, but I have noticed that very old books often offer "horrible" perspective examples that to contemporary eyes don't look all that awful. Apparently, our eyes have now become more accepting of images produced by wider lenses. Perhaps this has come about over the years by seeing so many news and television images made with quite short lenses at close distances.

9. ## Re: Portrait perspective: Quiz and two questions

Henry has it exactly right.

No need for maths and all the craziness.

Stand at a distance that you find the rendering of the subject to your liking. Choose a lens that provides the cropping that you want.

It is no more complicated than that.

It is also a mistake to get stuck into the idea that a certain lens/focal length/aperture/camera/film/filter (blah blah blah) must be used to accomplish something photographically.

something about skinning a cat.....

Look through the camera. When you see something that excites you, make a picture.

D.

10. ## Re: Portrait perspective: Quiz and two questions

hi jerry -

sorry, when it comes to photography, i rarely do math.
(i even cheat when it comes to computing bellows compensation)

i just stick a lens on the camera, and take the picture, otherwise i'd have to get a pad and paper and do long computations, and by the time i was done with the math, my subject would have fallen asleep.

why make things more complicated than you have to ...

-john

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