# Does 'focal length' mean something different with lenses and pinhole cameras?

Sometimes different but related things have the same name by some tradition or accident, causing a lot of headache to newcomers to a field.

I would like to come to clear terms with this: does the expression 'focal length' mean something distinct when applied to pinhole cameras vs. lens cameras?

With pinhole cameras it's the distance from the pinhole to the image plane. With lenses, it's the distance from the lens to the point where parallel incoming rays meet. Why are these things called the same? Am I right that this is just clumsy nomenclature or are these related at the limit of some infinities?

EDIT: Apparently some other diagrams label the lens-to-image-plane as "focal distance". Is "focal distance" something else than "focal length"? Or are people using inconsistent definitions? Something's fishy here.

• I think that people are just using "focal length" in different senses. The "focal length" of a lens is basically defined in the way you illustrated it in your 2nd picture. As for a "focal length" of a pinhole camera, I would say that, strictly speaking, there is no true "focal length" since it doesn't have any lenses which bring light into focus anywhere. However, I can also see how one might naturally use the term "focal length" to describe the pinhole-to-image distance in a pinhole camera.
– user93237
Dec 12 '15 at 23:26

Focal length in Physics is a property of a lens usually labeled $f$. It doesn't depend on the distances to the object or image involved (though you may determine if from that information).

The distance from the lens to the image is the image distance, often labeled $q$ or $d_i$. If it's positive, there is a real image and that is where the film or sensor should be.

A pinhole camera doesn't have a lens. It has a focal length of $\infty$. This leads to a virtual image (negative $q$), but the pinhole gives it such a huge depth of field that you call place the film anywhere and get focus as if you had a real image.

• Just for fun: Canaletto uses a pinhole camera to make sketches. Dec 13 '15 at 8:42
• As a rule of thumb the focal length of a pinhole (for visible light) is (hole diameter^2 * 550) in mm Sep 5 '17 at 21:38

While your sketch is correct, its scales may confuse you in this case. Do remember that, denoting the distances from the lens to the object and image plane by $$z_o$$ and $$z_i$$, respectively, we have $$\frac 1f = \frac{1}{z_o} + \frac{1}{z_i}.$$

Now in real world scenes, usually the camera dimensions are very small, so that $$z_o \gg z_i \Rightarrow f \approx z_i.$$ This means that a lensed camera with "focal point" at a distance $$f$$ from the lens can be geometrically thought of as a pinhole camera with "focal length" $$f$$. Of course the main difference is that since the lens in fact focuses many rays from the object to the same point on the image plane, the resulting intensity will be much higher. This approximation is very useful, however, when you try to figure the directions distances towards photographed objects.

• The sketch is not correct. The lower part is not correct because it does not show how the lens focuses the light. If it did show how the lens focused the light, then it would be obvious that the focal plane shown in the sketch is in completely the wrong place. The focal plane is where the film is located, and the focal length is the distance from the lens to the film. The upper part of the sketch is wrong because a pinhole does not focus light at all, and therefore it has no "focal length." Dec 6 '18 at 17:33
• @SolomonSlow The sketch is correct. You may be mixing up two true things: 1) parallel incoming rays meet at the focal point (not on the film) and 2) non-parallel incoming rays starting at a particular object point in focus will, on the other side of the lens, meet on the film. Also, it is common terminology in computer vision to say that pinhole cameras have "focal length", but it is indeed somewhat sloppy. A pinhole camera having focal length f just means that a lensed camera would need to use focal length f to focus an object at infinity to the same image plane that this pinhole camera has. Jun 25 '20 at 17:24