What is that diagonal formula ?

R

ruben

Guest
Somewhere someone said that the diagonal of the film frame equals the "normal" or "standard" focal legth of the lens for such frame.

I am more than weak in Maths, but if let's apply this formula to our most used film format, 135mm. So (24mm X 24mm) + (36mm X 36mm) equals a number whose square root will give us the size of the diagonal in our 24 x 36 frames.

The result is puzzling: 43,26mm ! This 'should be' the standard (?), natural (?) focal length for our 135mm film.

Of course we are talking here only about the formalistic mathematical side of the problem. Each of us has his own vision standards, which is not my intention to challenge.

Nevertheless this 43,26mm keeps me thinking. The camera industy has 'educated' us to believe that the standard-natural-normal-middle of the way focal length is 50mm. And by the same rule we have been told that a 40mm lens is a semi wide. The 45mm focal length has been rather a temporary exception, giving place to a very small Flickr group.

So I will throw my guess about the 43,26mm issue, or if you want "the diagonal formula".

In my opinion the 43,26mm focal length is indeed the standard mathematical vision - or if you like - focal length for the 24x36 format. The problem is not in the formula but in the format itself.

The 24x36 frame is, despite a century of photography, a somewhat un-natural format, a slightly too wide format, requiring a natural semi-wide vision to capture it.

The fact is that many photographers regard an uncropped print as a matter of excellency or skill. And I think it is, in non aesthetic parameters.

The 50mm focal length is more natural, or naturalistic if you like (in the sense of primitive), leading us to crop our negs, most of the times at the 36mm too large side.

Just my opinions.

Ruben
 
How about format orientation, Ruben ? A 35mm lens shot in portrait mode, has the same ("normal") horizontal FOV as a 50mm lens shot in landscape mode .... What is more "naturalistic", portrait or landscape format ?

And then there is paper, too. DIN fits 24x35 exactly. 6x4, 5x7, 8x10 are all dramatically different in aspect ratio.
 
Last edited:
"the diagonal of the film frame equals the "normal" or "standard" focal legth of the lens for such frame."
I'm not sure how seriously this must be taken, Ruben. To me it sounds like 50% coincidence and 50% mysticism with numbers.
Additionally, the viewing distance should also be included in the calculus somehow (i don't know how). If you look at a wider angle image from closeby, the perspective clicks into place and it does not look wide, it looks "normal".
 
Blame it on the movie industry. The 50mm focal length by our standards is way too long for the single frame format of 18x24mm, but I guess the needs of the motion picture industry didn't match ours. At any rate, when the first still 35mm cameras were made (Thanks, Oscar) it made sense to just pull a lens off the shelf to stick on the new camera. We've been stuck with it ever since.
 
"The fact is that many photographers regard an uncropped print as a matter of excellency or skill. And I think it is, in non aesthetic parameters."

Horse hockey.

You capture a moment with the equipment in hand, and you fill the frame as best you can. Sometimes, the resulting image is just fine uncropped; sometimes, a bit of judicious cropping definitely strengthens the image.

An interesting moment on this planet need not of necessity present itself in 2:3 aspect ratio merely because you happened to have a 35mm camera in your hand at that moment. Imagine that a friend is with you, and captures the exact same moment with a 6x7 camera. One of those two images is apt to be better with some cropping.
 
It may be relevant that several 35mm cameras were made which gave exposures whose longer sides were shorter than 36mm. For myself, I would prefer 32mm by 24mm to the "Leica standard". [edit] That would give a somewhat shorter diagonal, but I would keep to the focal lengths to which I am accustomed.
 
Last edited:
ruben said:
The result is puzzling: 43,26mm ! This 'should be' the standard (?), natural (?) focal length for our 135mm film.
Click to expand...

You are correct. And early designs also included 45mm lenses, which were quite common on fixed-lens rangefinders.

However, there was also a need for speed - and the Tessar design doesn't provide it.

Early SLR manufacturers found it easier to apply the double-gauss optical formula to a lens of slightly longer focal length, beginning with 58mm. 55mm was next, and finally 50mm. This was accepted as the 'best' lens design for double-gauss which was also sufficiently 'fast'.

You will note that very few 43mm lenses use the double-gauss lens design, and hence, are generally somewhat slower than f/1.4 to f/1.8. In fact, a 40mm lens is almost always a Tessar design.

I believe Pentax has made a 43mm lens, have they not? Sort of a collector's item.
 
Pentax has a 43mm LTM lens, and (without being able to proove it), I personally believe the CV 40/1.4 is, in reality, 43mm as well.

Not sure why you mention SLR lenses, Bill. For decades "50"/1.5 Sonnars and Planar/Xenotar based lenses were the fastest "normal" lenses, coming in 50, 55, and 58mm flavors. The first 1.4 normal lens was the Nikkor 50/1.4, released in 1950, also a Sonnar variant.

Best,

Roland.
 
ferider said:
Pentax has a 43mm LTM lens, and (without being able to proove it), I personally believe the CV 40/1.4 is, in reality, 43mm as well.

Not sure why you mention SLR lenses, Bill. For decades "50"/1.5 Sonnars and Planar/Xenotar based lenses were the fastest "normal" lenses, coming in 50, 55, and 58mm flavors. The first 1.4 normal lens was the Nikkor 50/1.4, released in 1950, also a Sonnar variant.

Best,

Roland.
Click to expand...

Hmm, good point. I'll think about that one, but I suspect you're right and I'm wrong.
 
The 135 format diagonal is 43mm, all right. IMHO, the 40mm CV or Summicron is a good, all-round focal length (as is 35mm). I think of lenses in that range as the "Natural Vision" field of view. My natural vision, that is--not necessary someone else's. I think bmattock is right: 50mm lenses became the de facto standard because they were easier to implement at the time.

History shows that it's possible to compose a good picture in any format, from the square format of 6x6 rollfim to the 2.54:1 aspect ratio that Cinemascope originally was. Add to that the XPAN format, which is even wider. I have no problem with the 3:2 format of most 35mm cameras. But then, I'm a wide-angle freak. I crop some 35mm pictures to 2:1 for projection on a screen of that same ratio. And I often print my black & white stuff at around 6.5 x 9.5 inches to use the whole negative.
 
the pentax fa limited 43mm is available new for Pentax SLRs, the LTM mount version with external viewfinder was actually very limited.

i love it on my slr
 
Many RF users consider the 35mm as their "normal" lens, so in this case one could consider the long side of the frame as equal to normal focal length... 36mm in the instance of 24x36mm frame. And 55mm for 6x4.5 and 6x6, 70mm for 6x7...

I have both types of Pentax 43mm lenses; KAF mount and L39 mount. This 7-element design is very similar to Zeiss Planar lenses intended for SLR use, and like Pentax's 50mm, 77mm and 85mm lenses.

Below: Pentax 43mm, Pentax 50mm f/1.4, Zeiss Planar for SLR.

attachment.php
 
Last edited:
Many simple fixed lens cameras are 35mm or 28mm focal length.

I'm using a Nikon 28mm lens camera right now.

Due to the generosity of Pitxu.
 
Doug said:
Many RF users consider the 35mm as their "normal" lens, so in this case one could consider the long side of the frame as equal to normal focal length... 36mm in the instance of 24x36mm frame. And 55mm for 6x4.5 and 6x6, 70mm for 6x7...
Click to expand...
For me, 55mm on MF and 35mm on small format are very different animals.

If I compare shots between 6x6 shot with 80mm and small format shot with a 35mm lens, particularly these feel equally 'spacious'.. And I think this comes from the ratio of the focal length to the short side. 35mm is 1.4x the short side of 36x24mm. Just as for 6x6, the standard lens (80mm) is 1.4x the side of a 56x56mm frame.

And that's why I've a hunch that the reason many consider the 35mm a "normal" lens is that they're judging it by the short side of the 36x24mm neg.

But if you're using the 1.4x rule on the long side of the small format neg, then all of a sudden a 50mm (which is 1.4x 36mm) doesn't seem so far out anymore as a "normal" lens.. In other words, for both 35 and 50mm lenses, an argument can be made that they're justifyably called "normal".

To me, the real difference between the 35mm and the 50mm focal lengths is that they behave differently when it comes to depth of field. The 35 can be scale focused; it is the hip-shooter's lens.. but at the expense of shallow depth of field. The 50 allows more isolation, and requires more careful focusing.

Yes, I know, subject isolation with a 35 is possible, just as guess focussing with a 50 is. But it's not their particular forte..
 
I display all my work full frame regardless. 40mm has always been my preferred focal length and is exactly what got me into rangefinders when I learned about the CL, which was my first leica. Its a shame there arent more 40mm lenses out there.
 
You must log in or register to reply here.
Back
Top Bottom