Why is Focal Length in mm (cm and inches), rather then Angle of View?

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Kirks518

Kirks518

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But wouldn't the design and the mount of the lens be the determining factor on how it will be used? If I manufacturer a lens that has a Pentax K mount, it's understood that it is intended/design for use on 35mm. If one chooses to use it on a different format, it would be up to that user to determine the new AoV based on the different format, much like is done now with the aforementioned 35mm equivalent.
 

Sirius Glass

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But wouldn't the design and the mount of the lens be the determining factor on how it will be used? If I manufacturer a lens that has a Pentax K mount, it's understood that it is intended/design for use on 35mm. If one chooses to use it on a different format, it would be up to that user to determine the new AoV based on the different format, much like is done now with the aforementioned 35mm equivalent.

But there are also lenses that are mounted on lens boards and those lenses may be used on a 6x9, 4"x5", 5"x7", 8"x10", half plate, full plate ... each one with its own field of view.
 
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And that could definitely be done. I gutted a Wirgin 6x6 folder. Used the lens affixing it with bellows to a MD lens mounting ring to fool around with me sr-T101. Also made a pinhole from the Wirgin.

AoV could become the new standard. There could be a new way to figure how a certain lens would cover a certain format. And it may happen in the future. Difficult to tell. Not saying it would not work. It would be a huge undertaking to rewire the understanding of millions of photographers.
 
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Kirks518

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I don't know if anybody ever answered this question; I apologize if I missed it here.

Focal length and aperture are a description of the product (a lens). Angle of view for the final image (as pointed out here) relates to camera size (or cropping). Cameras came in many sizes, and lenses could be used on most any of them, so the angle of view wasn't even known to the maker of the lens. This changed with cameras with dedicated lenses, but only for those cameras so still not a universal like focal length. With people regularly adapting lenses to different formats today, the situation is moving back toward what it was in the old full plate, half plate, etc days.

Now that's what I was looking for in the original question. Thanks Mark!

So (correct me if I'm wrong), back in the days of yore, a manufacturer would design a lens, and the targeted buyer of that lens may be using an 8x10, or a 4x5, or a 120 format camera, but the lens would be useable on all of them? Since there was no standard 'format' of film plane being used, something had to be standardized about the lens, so the focal point to film plane was chosen as the only thing really standard about a lens?
 

Mark Crabtree

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That's it. The focal length is the measurement of the lens.

A photography history book might be interesting reading. Not that it matters for this, but none of those sizes you mention were around in the days of yore when this started, particularly 120 since that is a roll film size. Seriously, it is enlightening to see how things came about. Like why it is called a "camera", how far back projecting an image on a surface goes, all kinds of interesting stuff.
 

L Gebhardt

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But wouldn't the design and the mount of the lens be the determining factor on how it will be used? If I manufacturer a lens that has a Pentax K mount, it's understood that it is intended/design for use on 35mm. If one chooses to use it on a different format, it would be up to that user to determine the new AoV based on the different format, much like is done now with the aforementioned 35mm equivalent.

I suspect early lenses and their measurement systems started out for large format cameras. There one lens can have a multitude of formats that it is compatible with. Focal length is constant whereas angle of view is dependent on the film size. Even medium format has the same issue, with the Mamiya RZ67 supporting 6x7, 6x6, 6x4.5 and maybe other sizes too. The angle of view would be different for each of the film backs with the same lens. It's a lot easier to buy a 65mm lens than it would be to cross reference each lens to the produced angle of view.

Also, since angle of view is proportional to focal length for a given format, if you know how one lens behaves, you will know how they all behave (in terms of angle of view).
 

smieglitz

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I must confess that I did not ponder every reply in the thread before writing this so maybe I missed something, but it would seem the relationship of focal length to f/stop simplifies the entire process of correct exposure and that might be the reason for having the familiar system in place. F/4 needs to be f/4 between various lenses and that number is dependent on focal length and the aperture diameter, not angle of view (AFAIK). The altitude of the right triangle that helps determine the f/stop value from the film diagonal (hypotenuse) could remain constant with an infinite number of angles of view, If so, I would think a system to determine proper exposure based on AOV would become nightmarish in terms of a calculation. Maybe not, but I think the traditional system is pretty simple and "if it ain't broke..."
 

ic-racer

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Why is Focal Length in mm (cm and inches), rather then Angle of View?
Because those are two totally independent variables and have nothing to do with each other.

Now you might correctly ask, why is lens coverage more often stated in millimeters rather than angle of view. Some manufacturers use millimeters for image circle and others use angle of view. To make comparisons easier, it would be nice to have both numbers.
 

Dan Fromm

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[rant]Hmm. Lessee now. Focal length is an attribute of a lens. It is the distance between the lens' rear node and the image plane when the lens is focused at infinity.

Angle of view is a loosely defined term that has several marginally compatible meanings.

One is twice the arctangent of ((half the diameter of the circle of good definition)/focal length)). Whatever the circle of sharp definition means. Focal length is as defined above.

This concept is well understood by people who shoot view cameras and similar types. You know the lens' focal length and maker's claimed angle covered, you know the diameter of the circle of good definition as defined by by its maker. You know the circle of sharp definition's diameter and the lens' focal length, you know the angle it covers. Big deal. They're equivalent. I hope its clear not all lenses that cover the same angle cover the same size circle. The longer the focal length, the larger the circle covered given focal length. Oh, my, there it is again. The linear measure focal length.

Another is used by devotees of smaller formats whose lenses come in focusing mounts and whose cameras offer no movements (no decentering, no swings). By assumption, not always true, lenses sold in focusing mounts have circles of sharp definition at least as large as the diagonal of the format the camera they fit shoots. People speak loosely about horizontal, vertical, and diagonal angles of view. All calculated as 2 * arctan((format's long side/short side/diagonal)/2 *focal length), and the format's long side is conventionally assumed to be horizontal. Focal length is defined as above.

The linear measure focal length as defined above is central to all these concepts

What we have here is an attempt to help people who grew up with auto-everything cameras (including but not limited to digital cameras) and never learned the basics. These are the idiots who say "if I adapt a Nikon lens to my Pen F the lens' focal length doubles." Except of course that people who use Pen Fs usually know very well what they're doing. People who use tiny chip digital cameras are another matter entirely. Let them learn the common language. [/rant]
 

Bill Burk

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The point has been driven home to me recently as I am looking to re-create Bill Brandt's signature wide-angle look. I've found that he used the Zeiss Protar f.18 8.5 cm. lens Serial No. 1355381

I've tried to find the equivalent angle of view for different formats and the corresponding lenses. But so far, I don't have a shopping list because the equivalents aren't up on a website somewhere for me to compare.

I recently saw an Angulon 90mm sell for a reasonable price here on APUG.

But I asked myself... Is 90mm wide enough? It's only 5mm "longer" so it might be. Except the Angulon is not the "Super" Angulon, so it would barely cover 4x5. And Bill Brandt was shooting "full plate" 6 1/2 x 8 1/2 inches... I shoot 4x5 inches.

This is the worst that has happened to me because of the convention. It's not that bad.
 

Chan Tran

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I think because long ago people used the same lens for different formats. The 210mm lens is always 210mm but the angle of view is quite different from 4x5 and 8x10 and many 210mm lens can be used for both 4x5 and 8x10.
 

bernard_L

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Restating what has been said differently. Take a lens. Just the lens. Give it to any qualified optician. He/she will measure the focal length of that lens. Unambiguous definition: ratio of lateral displacement in focal plane to angular displacement of object (at infinity).

Give ten identical copies of same lens to ten different photographers, using it with APS, FF, 645, 67, etc... sensors or films: so many values of angular field of view.
 
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Implementing Dan's second stated approach, here is a table listing the equivalent focal length lenses required to cover the indicated formats to the same angle-of-view (thereby showing roughly the same "scene" on each format) as a 50mm lens projecting onto a 35mm format frame. All of the assumptions mentioned by Dan are in play. The 50mm output line has been highlighted:

Kirks518.jpg



This was generated from a simple command line software utility I've been adding quirky things to for years now for my own use...

Ken
 
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lxdude

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But wouldn't the design and the mount of the lens be the determining factor on how it will be used? If I manufacturer a lens that has a Pentax K mount, it's understood that it is intended/design for use on 35mm.

Not true these days. It could be for either full full-frame or crop-sensor digital (FA versus DA). Similar with Canikony.

It's not as helpful as you might think, anyway. How many beginners could easily visualize a certain number of degrees, especially if on diagonal? They would want to see what the number of degrees looks like by looking at a picture. They still have to translate a certain number into what it means for the final image. It's as easy for them to grasp what a picture taken with a 50, 35, 200, etc. looks like, as to grasp what a certain number of degrees looks like. And they only really understand what they will get through experience with any particular lens, regardless of how the lens is described.
They could mark lenses with AoV today, even for more than one format. But there doesn't seem to be any particular demand for it.
 

Steve Smith

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The lens is always measured/specified as focal length. It is up to the photographer to use his/her own intelligence to work out how this applies to the equipment they have.

The point has been driven home to me recently as I am looking to re-create Bill Brandt's signature wide-angle look. I've found that he used the Zeiss Protar f.18 8.5 cm. lens Serial No. 1355381

I've tried to find the equivalent angle of view for different formats and the corresponding lenses. But so far, I don't have a shopping list because the equivalents aren't up on a website somewhere for me to compare.

I recently saw an Angulon 90mm sell for a reasonable price here on APUG.

But I asked myself... Is 90mm wide enough? It's only 5mm "longer" so it might be. Except the Angulon is not the "Super" Angulon, so it would barely cover 4x5. And Bill Brandt was shooting "full plate" 6 1/2 x 8 1/2 inches... I shoot 4x5 inches.

Using the long dimension of the film, 8.5" and an 85mm lens gives an angle of view of 104 degrees. On 5x4 the same angle requires a 50mm lens. That 90mm lens on 5x4 will give you 70 degrees.

angle.jpg

EDIT: I appreciate that you probably know this and I don't want to appear patronising but I posted it for the benefit of those who don't know. If you have use of a CAD program, it's easy to draw up a triangle like this using the film size and focal length and then measure the angle.


Steve.
 
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lxdude

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I think because long ago people used the same lens for different formats. The 210mm lens is always 210mm but the angle of view is quite different from 4x5 and 8x10 and many 210mm lens can be used for both 4x5 and 8x10.
Yes. When the convention began, it made complete sense, and designating by AoV made little sense.
 

Dan Fromm

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Actually, folks, in the beginning there were several competing conventions for describing a lens' focal length.

I think -- could well be mistaken -- that the first was the format covered. See, e.g., the 1868 price list that can be downloaded from http://www.thedallmeyerarchive.com/Records/catalogues.html The lenses' descriptions always give the size of the largest plate, sometimes give focal length and back focus as well.

Always mentioning focal length came in later. See, e.g., http://cnum.cnam.fr/CGI/redir.cgi?M11192 Once there, click on Exports, then on Télécharger ce document au format PDF The lens tables give focal length (distance focale) and format covered (Format normal). This convention persisted for some time, see, e.g., http://www.cameraeccentric.com/html/info/bauschlomb_2.html

Mentioning format covered as well as focal length is important for lenses that aren't in focusing mounts, e.g., many of the lenses offered for formats larger than 6x7. For lenses in focusing mounts that are tied to one format there's no need to be explicit about coverage. And that's no one mentions that lenses for 35 mm still cameras cover at least a 43 mm circle. [rant]Its understood by everyone but people who don't know very much.

Ignorant users of small format cameras are unaware of the basics and the history, make the common mistake of assuming that what little they know is all that's known and is universally true.[/rant]
 

frank

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Yes. When the convention began, it made complete sense, and designating by AoV made little sense.

And it continues to make complete sense in the present day.
 
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E. von Hoegh

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(Wasn't sure where to put this, as we don't have a 'Lens' Section, but since 35mm is the general public's standard, I figured I'd put it here.)

Now that I'm shooting MF as well as 35mm (and APS-C), this question has really been bugging me.

I understand that the focal length of a lens is determined by the distance of the focal point to the film plane, whether it be label in mm, cm, or inches. But when you change formats, what an Xmm lens captures changes from format to format. In other words, a 50mm lens on a 35mm format camera will capture ~46° of the scene. But a 50mm lens on a 6x7 will capture ~81° of the scene. Same focal point to film plane distance, but a completely different image results.

Now it can be said that the general public knows what a 'XXmm' lens will give them as a final image, but that's only because it became the standard way back when. I know for a fact that people new to photography have a difficult time grasping the difference between what they will get as a final between a 24mm, 50mm, and 135mm. Many just don't have any idea what that means, and I'm sure back in the day it wasn't any difference. There is no (IMO) logical relationship between 50mm and 46°, that can be (relatively) immediately understood by a novice.

But if I say to someone who has a basic understanding of geometry that your eyes see ~200° of a scene, and that lens A gives you an image that represents 81° of that scene, I think they might have a better comprehension of what the end result will be. They can take their hands, hold them up to their face, and make blinders that give a 81° view of the scene, and get an idea of what they'll get in their image.

I personally try and convert a 'mm' lens into AOV lens, so I can 'see' what I'll get without having to try different lenses. In other words, I'll look at a scene, and say to myself I want approximately 55° of what I am seeing to be captured, and then grab the lens closest to that.

Labeling a lens as a 52° AOV would standardize the entire lens lineups across formats. No matter what format you're using, a lens with an AOV of 52° will give you 52° of the entire scene. So, in my case, my 24mm (35mm format) lens would be labeled as 81° AOV, as well as my 50mm MF lens (Mamiya RB67). But the way it is now, I have two lenses that are named the same, but give 'wildly' different results.

Discuss.... :wink:

That would lead to confusion in many areas. The lens that gives a 50 degree AOV on 8x10 will give 25o on 8x10 and so on. Different format aspect ratios will result in different Aovs if the Aov is specified diagonally. Personally, I think specifying the focal length is the only way to go - and I'm not even going to address the Dof calculation (for which the focal length datum is essential) nightmare it would produce.
 

Nodda Duma

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As a lens designer the related spec I pay attention to the most is horizontal and diagonal field of view (or corresponding image heights if more pertinent).

I can tell you the FOV's or AFOV's of all the lenses I've designed going back a decade or whatever my memory can handle but can only tell you the focal lengths of a very few (not that I couldn't calculate it. I remember the image plane sizes too).

My typical customer is intimately more familiar with what different fields of view values look like than photographers (who correlate a field of view more naturally to a focal length) . Most folks who use optics for observation-type purposes typically are (astronomers, sportsmen, war fighters, etc). Focal length values would confuse them. All approaches are valid as long as you don't put fingerprints on the optics.

You're comfortable with what you're familiar with.
 
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Kirks518

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As a lens designer the related spec I pay attention to the most is horizontal and diagonal field of view (or corresponding image heights if more pertinent).

I can tell you the FOV's or AFOV's of all the lenses I've designed going back a decade or whatever my memory can handle but can only tell you the focal lengths of a very few (not that I couldn't calculate it. I remember the image plane sizes too).

My typical customer is intimately more familiar with what different fields of view values look like than photographers (who correlate a field of view more naturally to a focal length) . Most folks who use optics for observation-type purposes typically are (astronomers, sportsmen, war fighters, etc). Focal length values would confuse them. All approaches are valid as long as you don't put fingerprints on the optics.

You're comfortable with what you're familiar with.


Awesome!

So basically what I infer from your post is that essentially the rest of the world understands AoV/FoV, but only photographers understand and can relate to focal length. We're an odd bunch....
 

Sirius Glass

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[rant]Its understood by everyone but people who don't know very much.

Ignorant users of small format cameras are unaware of the basics and the history, make the common mistake of assuming that what little they know is all that's known and is universally true.[/rant]

And it continues to make complete sense in the present day.

And it will continue to make sense regardless of the digi-snapper in the know nothing media.
 

Sirius Glass

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Awesome!

So basically what I infer from your post is that essentially the rest of the world understands AoV/FoV, but only photographers understand and can relate to focal length. We're an odd bunch....

Of course we are an odd bunch. We use film.
 
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Kirks518

Kirks518

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Initially, I wasn't suggesting anything, but I was curious as to why the system we know was settled on. At the time, lenses were designated with focal lengths in millimeters, centimeters, and inches. Why mm, and why not cm or inches? And with (at the time) there being 3 different designations (or more), why didn't they just abandon the FL, and not go with AoV. That has been answered earlier.

But now that I've been thinking about it, IMO, it would make more sense to use AoV (for the format the lens was intended to be used on), and it would be easier for a layman to have an understanding of what each lens will give them in their final image (as supported by the statement above).

But I'm happy to continue with the old (current) system, although I liken it to using cubits to determine fuel economy when all (standard) distance measurements are in miles or kilometers - 'My car gets 88,000 cubits per gallon!' (that's 25mpg if you're wondering.

Everything changes over time. Some will be accepting of a change, others will fight it tooth and nail. Such is life....
 

E. von Hoegh

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Initially, I wasn't suggesting anything, but I was curious as to why the system we know was settled on. At the time, lenses were designated with focal lengths in millimeters, centimeters, and inches. Why mm, and why not cm or inches? And with (at the time) there being 3 different designations (or more), why didn't they just abandon the FL, and not go with AoV. That has been answered earlier.

But now that I've been thinking about it, IMO, it would make more sense to use AoV (for the format the lens was intended to be used on), and it would be easier for a layman to have an understanding of what each lens will give them in their final image (as supported by the statement above).

But I'm happy to continue with the old (current) system, although I liken it to using cubits to determine fuel economy when all (standard) distance measurements are in miles or kilometers - 'My car gets 88,000 cubits per gallon!' (that's 25mpg if you're wondering.

Everything changes over time. Some will be accepting of a change, others will fight it tooth and nail. Such is life....

All have been used. I have 5cm, a 3.5cm, and an 85mm lenses for my Kievs. The 85, made in 1970, would have been marked 8.5cm if it were an earlier lens such as the other two. Early CPG Berlin Dagors were marked in mm, later ones in cm. New York Dagors were marked in inches, as were Kodak Ektar lf lenses until they ceased production. My Kodak 35rf with Kodak Anastigmat "Special" lens from 1940/41 was marked in mm, though.
I use formats from 35mm to 8x10 and most in between. It makes no sense to mark a lens with Aov when I might be using it on 6x7, 4x5, 5x7 or 8x10.
Besides, after 40 or so years I know what the lens will do on various formats - and if I forget I have only to look in the viewfinder or on the groundglass. :wink:
 
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