Question: Angle of View and Focal Length

[JKSinMB]

I thought there was a mathematical relationship between focal length, film/sensor format, and angle of view. In other words, two lenses with the same focal length will have the same angle of view when used on any given camera.

While looking at Canon’s lens specifications, I learned that this doesn’t hold true for their lenses. For instance, the 17-40L has a reported angle of view of 74° to 29°, while the 24-70L also has a reported angle of view of 74° to 29°. Meanwhile, the two 24mm primes have an angle of view of 84°. While this example really stands out, there are other examples throughout the specs page.

http://www.usa.canon.com/html/eflenses/pdf/spec.pdf

I have decided that my definition of angle of view must differ from Canon's. Can someone please explain this to me.

Thanks.

[Scottes]

I can't explain it fully but I'm sure it has something to do with the size of the elements. Is the filter size the same for all those lenses?

I would assume that a 20mm with a 77mm front element would have a wider field of view than a 20mm with a 52mm front element.

[JKSinMB]

After looking at the specs page a little more, I've realized it's only the 17-40L and 24-70L that have inconsistent angles of view for their focal lengths. Each of the other examples I thought I had found included one of these lenses as part of the comparison. Thanks for the post Scottes, but I think the answer to my question is that the specs page contains typos for these two lenses.

[Belmondo]

Check here.

http://www.sweeting.org/mark/lenses/

It takes into account sensor size, as well as all the Canon lenses.

[AJSJones]

I thought there was a mathematical relationship between focal length, film/sensor format, and angle of view. In other words, two lenses with the same focal length will have the same angle of view when used on any given camera.


I have decided that my definition of angle of view must differ from Canon's. Can someone please explain this to me.

Thanks.

Your first sentence is true but you stopped thinking about film/sensor format after that!
Different lens designs with the same focal length can create different sized "image circles" All you really need is an image circle that covers your sensor/film format size. If the image circle is smaller than that , that lens has a narrower angle of view, while one which projects a larger image circle will have a wider angle of view. To help visualize this, you could get a lens designed for 35 mm film and its image circle would not cover a sheet of 4x5 film, even though it's the same lens with the same focal length. Correspondingly, a lens of the same focal length designed for 4x5 may not fill a sheet of 8x10 film. How much of the "angle of view" of a particular lens will be captured depends on the format of the device you use..... If you buy a "digital lens" that was designed for smaller sensors, its image circle may not fill the 35mm frame because its image circle is too small.
This is the same issue about a 10D sensor being smaller than a 35mm frame - some call it a magnification factor, others a crop factor, yet others object to one or other or both of these terms. I call it a format factor .

Andy

[RichardtheSane]

Personally it looks to me like a typo :D

(always looking for the simple answer :D )

[sdommin]

Personally it looks to me like a typo :D

(always looking for the simple answer :D )

Sometimes the simple answer is the best! I believe it is a typo. I have both lenses, and the instruction booklets give the following info:

17-40L Angle of view-

Diagonal: 104° - 57°
Vertical: 70° - 34°
Horizontal: 93° - 49°


24-70L Angle of view-

Diagonal: 74° - 29°
Vertical: 53° - 19°
Horizontal: 84° - 34°

(Some figures rounded for clarity)

[EXA1a]

Check here.

http://www.sweeting.org/mark/lenses/

It takes into account sensor size, as well as all the Canon lenses.

I really like that sweet calculator. However, I found one error: the Sigma diagonal fisheye (15/2.8) calculates like a rectlinear lens which it isn't. A FE has a wider AoV (~90° horizontally for 15mm) than its rectlinear pendant (~74°) of the same FL.

--Jens--

[hmhm]

I thought there was a mathematical relationship between focal length, film/sensor format, and angle of view.

There is, of course. Errors in the Canon web site specs are common.
-harry

[marksw]

Check here.

http://www.sweeting.org/mark/lenses/

It takes into account sensor size, as well as all the Canon lenses.

I really like that sweet calculator. However, I found one error: the Sigma diagonal fisheye (15/2.8) calculates like a rectlinear lens which it isn't. A FE has a wider AoV (~90° horizontally for 15mm) than its rectlinear pendant (~74°) of the same FL.

--Jens--

Well spotted! I removed the shorter fisheye lens, but failed to realise that they had two. Thanks for drawing my attention to it, and for the kind words :-)

Cheers,

Mark

[iwatkins]

Mark,

Any chance you could add the Sigma 12-24mm to the list ?

Cheers

Ian

[marksw]

Any chance you could add the Sigma 12-24mm to the list ?

I think so Ian... ;-)

Is this a new lens? I am surprised I missed it!

Anyway, I've added the 12-24mm F4.5-5.6 EX Aspherical DG / DG HSM to the calculator.

All the best,

Mark

[iwatkins]

Thanks Mark,

You are a star 8)

Yes, fairly new lens so probably wasn't spec'ed up when you put the calculator together a while back.

I find it especially useful for working out how many shots I need to take, and at what angles, to put together 360° panoramas. Great tool.

Cheers

Ian

[marksw]

No problem Ian - I aim to please :lol:

In fact I appreciate it if people let me know of errors and omissions. That way I can keep the tool up to date and accurate so that it is more use to everyone.

Cheers,

Mark