[Class A]

In a linear-log plot (cf. my post above), this is the exact middle between the two inflexion points

Seems to be a very appropriate plot form.

See the wikipedia entry for "Normal lens".

But does anybody know why everybody else including Pentax non-limited proposes 50mm? What is the history behind this?

The 50 mm focal length was chosen by Oskar Barnack, the creator of the Leica camera, as a compromise between the theoretical value and good sharpness, as lens technology at the time was such that slightly longer focal lengths were able to achieve optimum sharpness.

EDIT: BTW, Pentax lens designer Jan Hirakawa refers to the same definition of "normal" focal length. This translation was referred to from a DPReview discussion.

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Last edited by Class A; 05-26-2010 at 03:44 PM.

[rparmar]

I don't think this formula for AOV has anything to do with the definition of "normal", even if the term was used to refer to a natural viewing angle. It is directly related to the diagonal, and since the diagonal shows up in the above formula there is some inter-relationship.

I have seen no reference for that Barnack quote, though it is oft repeated. A more reasonable explanation derives from actual 35mm film strips. If you find the diagonal of 35x35 you get 49.5mm.

50mm was a comfortable length for designing optics since at least 1924 when Ludwig Bertele came up with the Sonnar. I have no idea when the term "normal" was first used.

[rparmar]

OK, I found some sort of a reference from Leica to the whole normal thing. This PDF is fascinating!

Erwin Puts 50-60mm Leica R Lenses

[Class A]

I don't think this formula for AOV has anything to do with the definition of "normal", even if the term was used to refer to a natural viewing angle.

There is a relationship in that there is an assumption that one will look at an image from a distance that corresponds to the image diagonal.

If we were to look at images from a distance twice as large as the image diagonal, then f=2d would define the normal focal length.

Think of the situation of viewing an image as a reversed and scaled up version of the recording situation. Only if the relative proportions of image size vs sensor size and viewing distance and focal length respectively are maintained then you get a view on the image that preserves the perspective distortion you would have observed if you had been in the scene exactly in the place where the camera was. Choose another focal length or viewing distance and the perspective distortion will be different. This property makes the "normal" focal length special, and yes, a non-standard viewing distance destroys the property.

If you find the diagonal of 35x35 you get 49.5mm.

But who shoots 35x35 images?

OK, I found some sort of a reference from Leica to the whole normal thing.

Thanks for the pointer. I haven't read the whole article yet but it starts off in an odd way. The author writes

[i]
The length of the diagonal of the 35mm-format is 43mm (to be precise: 43.27mm) and therefore this should actually be its focal length. ...
More important from my point of view are the perspective and angle of view that one gets with a 50mm lens.

The "more important" bit doesn't make sense since the two aspects are two sides of the same coin.

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Last edited by Class A; 05-02-2010 at 07:23 AM.

[falconeye]

There is a relationship in that there is an assumption that one will look at an image from a distance that corresponds to the image diagonal.
[...]
Thanks for the pointer. I haven't read the whole article yet but it starts off in an odd way.

I am sure we're having a hundred year old discussion but it's fun

First, let me repeat that the "normal" focal length is not purely about a concept. The normal focal length is one where, if you look with one eye through the VF and with another one directly, both images would overlap. Some (few) photographers really do this to frame their images...

E.g., a Pentax MX (0.97x magnification with 50mm) and Pentax ME and LX/FB-1/FD-1 (0.95x magnification) use 52mm as this normal. With the K-7, it's 54mm (**).


Do we really look at an image at ~diagonal distance? I'll have to observe this
At least as for watching TV, it seems to be wrong. E.g., a 50" screen is typically watched from 2.5m to 4m viewing distance which is exactly 2-3x the diagonal. Official recommendations vary between 3-5x. I think 3x is the smallest where no head turns are required to capture all parts of an image with equal attention.

2,3,4x the diagonal is 28°,19°,14°.

3x with 16:9 is 16.5° x 9.3° (16°x9°) which is really really easy to remember

According to the nice link to the Leica article, the human's field of view spans 200° x 140° (240° diagonal if the field of view were rectangular).

So, the human vision is better characterized by a 200° (8mm) FishEye combined with a 14° (180mm) Tele.

I find it challenging to define the "normal" for a 8-180mm double-focal lens. This is why I was asking.

At least, the geometric mean between 8mm and 180mm is 38mm which is close enough to the image diagonal rule. Still, looks rather arbitrary to me. Which is why I said I would appreciate any "official" source for the "50mm is normal" tradition.


____
(**) If I try it with K-7+60mm (easiest in portrait orientation) I find that the K-7 image is indeed almost exactly as large as the naked eye vision. The published 0.92x magnification is meant without any crop factor correction (54mm for overlapping images).

The double-eyed composition is really cool. I see black frame borders in the middle of the entire scene which I am still continuing to see. Unfortunately, the large camera body obstructs one half of it. An electronic viewfinder clipped onto one eye (monocular) could be a cool gadget

[Digitalis]

"An electronic viewfinder clipped onto one eye (monocular) could be a cool gadget"

- I think you would have people screaming and running away in fear of being assimilated.

[Class A]

The normal focal length is one where, if you look with one eye through the VF and with another one directly, both images would overlap.

As you mention this depends on the VF magnification and hence, IMO, in practice becomes a bit arbitrary.

Do we really look at an image at ~diagonal distance? I'll have to observe this

This assumption is meant to apply in the case of still images.
Your TV example is similar to the situation in a movie theatre where the viewing distance is much larger. Accordingly, the "normal" focal length for a cinema camera is ~ twice the image diagonal, not ~ the image diagonal.

I find references to the AOV(s) of the human eye in this context not very helpful. The AOV(s) of the human eye are difficult to define because of the irregular shape of the field of vision and because there is a difference between peripheral and central vision (which even seems to differ between individuals). Therefore, the only hope to have a clean definition of "normal" w.r.t. a focal length is one that is based on preservation of perspective distortion.

I use "perspective distortion" in the sense that nearer objects appear larger, in other words, even a "normal" lens produces "perspective distortion" it just happens to be the one that one would have experienced in the same place as the camera was in. Another way to use "perspective distortion" (which I used earlier but is apparently incorrect) is to refer to the angles reproduced by the "normal lens" as undistorted and the angles produces by a wide-angle and telephoto lenses (when positioned in a way to yield the same FOV) as distortions in the form of "angle exaggerating" and "perspective compressing" respectively.

I think you would have people screaming and running away in fear of being assimilated.

Their resistance is futile.

N.B., was the graph I provided what you were looking for?

[rparmar]

But who shots 35x35 images?

That is the full size (including sprockets) of a 35mm film image. In the early days still photo lenses were often manufactured by cine houses and the work done in cinema drove still lens production. It was cheaper for Leica to leverage their cine lens experience and so came up with 50mm as the normal length, which it is if certain assumptions about film are made. 50mm also offered a nice view to the eye, and is a nice round figure so it stuck. (Note that many so-called 50mm lenses are actually a bit longer.)

I haven't read the whole article yet but it starts off in an odd way. The author writes

The length of the diagonal of the 35mm-format is 43mm (to be precise: 43.27mm) and therefore this should actually be its focal length.... More important from my point of view are the perspective and angle of view that one gets with a 50mm lens.

The "more important" bit doesn't make sense since the two aspects are two sides of the same coin.

Well, yes and no, since the "eye feel" depends on the magnification in the viewfinder (if one has a viewfinder). As Falk says:

The normal focal length is one where, if you look with one eye through the VF and with another one directly, both images would overlap.

What would make absolutely the most sense is if 43mm was the normal length and the viewfinder magnification was set so that this produced a perfect image correspondence. Does anyone know of a camera for which this is true?

[rparmar]

Bizarre how all these threads end up being about what "normal" is.

[rparmar]

I think you would have people screaming and running away in fear of being assimilated.

They already do that around me.

[Class A]

That is the full size (including sprockets) of a 35mm film image.

Seems irrelevant for the discussion. Even if there is a connection between Leica and cine lenses, even the latter weren't used for a square 35x35 format.

Well, yes and no, since the "eye feel" depends on the magnification in the viewfinder (if one has a viewfinder).

I'm convinced the author did refer to the "perspective and angle of view" of the final image, not the view through a viewfinder.

What would make absolutely the most sense is if 43mm was the normal length and the viewfinder magnification was set so that this produced a perfect image correspondence.

This would be nice but the crucial bit is the correspondence between the FL and the sensor size. The viewfinder magnification just concerns (temporary and for the viewer of the final image irrelevant) image size, not perspective distortion.

[rparmar]

Seems irrelevant for the discussion. Even if there is a connection between Leica and cine lenses, even the latter weren't used for a square 35x35 format.

Yeah, I know.

But nonetheless that's where it came from. According to the references we actually have.

[Digitalis]

According to the information I found the original 6x4.5 format is 56mm x 41.5mm. The 645D uses a 44mm x 33mm sensor. This results in a crop factor of 1.27 and the following...

According to the Dpreview article on the new D-FA645 55mm f/2.8 they quote the FOV as "43.5 on a 35mm equivalent". Or am I confusing the AOV of 35mm equivalents with medium format ones?..I wish Pentax would just cram a full frame 645 sensor in it and call it what it is...maths has never been my strong point (I'm a musician)

[Class A]

According to the Dpreview article on the new D-FA645 55mm f/2.8 they quote the FOV as "43.5 on a 35mm equivalent".

Here's the dpreview text

When mounted on the PENTAX 645D camera body, this standard lens offers a focal length of 43.5mm (in the 35mm format), which produces an angle of view close to that of the human eye.

They express the 55mm on the 645D in terms of a lens on an FF camera. Both a 55mm on the 645D and a ~43.5mm lens on FF produce an AOV of 53.13°.
And indeed in both cases the focal lengths of the lenses is very close to the sensor diagonal so they can be counted as "normal lenses" that produce a natural perspective distortion.

Or am I confusing the AOV of 35mm equivalents with medium format ones?

I guess that's what you did.

..I wish Pentax would just cram a full frame 645 sensor in it and call it what it is...

In this case the standard lens for it would have been a 70mm lens.

[kacansas03]

I have noticed that field of view for a particular lens can be affected by the build of the lens. On one of my long focal length lenses the extremely large size of the whole lens results in about a .75 increase in FOV compared to the usual. Also on another lens the small diameter of the lens down the whole barrel gives it slightly narrower FOV. These are older screw mount manual lenses and I do not think this would be the case on modern lenses. But I am wondering if anyone else has noticed any large differences from what would be the 'norm' for a particular focal length, not counting purpose built fish eye lenses.
I really wish to thank those of you, rparmar and Class A, who have gone to all the trouble to do the research and plot the graphs then share it with the rest of us. I found the article about the Leica lenses very interesting. Thanks again.