FAQ: Focal length, field of view and formats

[Laurent Andrieux]

The focal length is, by definition, the distance from the lens (considering a thin lens) at wich the image of an object placed at the infinity will be sharp.

 

The focal length is then only depending on the lens carachteristics.

 

According to the size of the lens and mount, one lens will fit a camera and format, or not.

 

The format of the image is given by the aperture plate of the camera (film) or the usefull dimension of the pick-up device (video)

 

The field of view can be given in 2 different ways :

 

1) Object size : at a given distance, the frame will cover a certain height and a certain width. It depends on the focal length and the image size, wich is given by the format.

 

The relationship is therefore : DXI = OXF where D is distance from camera to subject, I is the image size, O is the object siez or covered Width/heigth at the given distance D, and F the focal length.

 

2) Angle of view : if you consider A the angle of view, then, tan(A/2) = I/2F where I is the image size, either height or width and F the focal length.

 

so, when you have I and F, calculate I/2f = tan(A/2), let's say, the result is R, make sure your calculator is in degrees, compute tan^-1 ® or INV tan ® according to your calculator as to have the inverse function of tan , then you get A/2, multiply by 2 and you get A

 

In another post, I'll give you the common image sizes for different common film and video formats

[Aaron Solomon]

I thought focal length was the distance from the back of the lens to the film/CCD? Not the object being filmed, which is what you seem to be saying.

[Simon Wyss]

The focal length is, by definition, the distance from the lens (considering a thin lens) at wich the image of an object placed at the infinity will be sharp.

If I may adjust a little: The focal length of a lens is by definition the distance between it and the image plane when said lens is set to form the sharpest possible image for an object at infinity. The very base of all lens geometry considerations is the idea of an infinitely small hole or aperture in the CAMERA OBSCURA. Light from all objects would fall through the aperture onto the camera’s image surface, infinitely sharp but infinitely weak.

 

From idea to life we make the hole of finite size. That is the pinhole camera.

 

Adding optical elements of higher refractive power than air is the beginning of solid optics. Things become already complicated with a single lens. In the case of a symmetric lens the so-called optical plane lies in its centre. As soon as we depart from symmetric forms the optical plane will move. The focal length will no more be identical to the actual distance lens-image. As a matter of fact, the shift is very small.

 

It is simpler to produce small lenses and precision more easily attained for such but resolving power bigger with larger aperture lenses. Each and every optical lens is the product of compromises. Focal length is perhaps the cheapest ingredient: longer focal length generally helps in the design of an optical system.

 

On the other hand, the wider we make the aperture the more difficulty shall we have with the light coming to the lens toward its rim. At f/0.5 these light beams just graze the glass surface under a horrible angle. This in turn decreases the size of the usable image surface. The focal length should be short for this reason.

[Brian Drysdale]

Abel Cine have this for comparing fields of view

 

http://www.abelcine.com/fov/

 

You can't always have the focal length being the distance from the back of the lens, otherwise you couldn't use mirror shutters on short focal length lenses. The retro focus design (seen on Distagon lenses) overcomes this.

[Brian Drysdale]

There's a Mitch Gross video on focal lengths and formats:

 

http://blog.abelcine.com/2010/05/14/a-lens-is-a-lens-is-a-lens/

[Carl Looper]

I'd define focal length this way:

 

The focal length is just the distance between the lens and the imaging plane regardless of focus.

 

The focal length otherwise inscribed on the lens is just that particular focal length (lens to image plane distance) at which an object at infinity would be in focus.

 

But a lens can be placed at any distance from the imaging plane, and this distance will be the focal length.

 

 

C

Edited June 25, 2015 by Carl Looper

[Mark Dunn]

The focal length is just the distance between the lens and the imaging plane regardless of focus.

1) No. if anything that would be the extension.

 

The focal length otherwise inscribed on the lens is just that particular focal length (lens to image plane distance) at which an object at infinity would be in focus.

2) Yes.

 

But a lens can be placed at any distance from the imaging plane, and this distance will be the focal length.

3) No. See 1.

[Simon Wyss]

Men, it depends on the lens design.

 

With a so-called fixed focal length lens, things are as Carl says, and the lens doesn’t care what distance we set it at. The manufacturer knows the exact value of FL of his system. I once had a projection lens measured by the manufacturer because I wanted to know about the difference between paper and glass. Schneider Ciné-Xenon 30 mm had in reality 30,4 mm FL. (We employ the decimal comma)

 

With variable-focal length lenses, and here again depending on the various ideas, it is rather complicated. In a triplet with front-element focusing I actually change FL (a little) when I turn the ring. With catoptic systems, mirror lenses, things can look even weirder. But frankly, my dears, I don’t give a damn.

[Carl Looper]

The focal length is not a property of the lens. It's a measurement one can make of where the lens has been positioned with respect to the imaging plane. The distance between the two.

 

When speaking of focal length we need to clarify what we mean by "lens". After all, the barrel of a lens has a length. At what point along the barrel of a lens does one use as the measurement point? Depending on design this point can also vary as various elements are positioned.

 

The solution is that lenses are elaborations of a pin hole model.

 

In a pinhole camera the point in question is the centre of the pin hole. The distance between the pinhole and the imaging plane is the focal length. To vary the focal length in a pin hole camera is to vary the distance between the pin hole and the imaging plane. The pin hole is the centre of projection for the image.

 

So in a lens, to vary the focal length is to vary the distance between the lenses centre of projection and the imaging plane.

 

If this wasn't the case the following equation from the pinned FAQ would not be as general and all encompassing as it is:

 

2) Angle of view : if you consider A the angle of view, then, tan(A/2) = I/2F where I is the image size, either height or width and F the focal length.

[Carl Looper]

[Carl Looper]

The focal length is just the distance between the lens and the imaging plane regardless of focus.

1) No. if anything that would be the extension.

 

An extension is literally an extension of the focal length to a new focal length, ie. extending the distance between the lens (it's centre of projection) and the imaging plane to a new distance. The new distance becomes the new focal length and this new focal length can be used in angle of view calculations that require focal length as a parameter:

 

 

 

C

Edited June 26, 2015 by Carl Looper

[Simon Wyss]

Are we repeating each other?

[Mark Dunn]

:wacko:

[Carl Looper]

Are we repeating each other?

 

Not so much repeating each other as demonstrating that, although our voices differ, there is agreement between them - an in common logic to such. That what is being discussed, while it might be interpreted as personal opinion, is better interpreted as a shared understanding.

 

cheers

C

[Simon Wyss]

[Don H Marks]

This is the table for Regular-8 to which I refer when focal length discussions come up. 

For simplicity the numbers are rounded and the field of view used is the diagonal of each format's film gate. 

 

Edited March 31, 2024 by Don H Marks

[David Lawson]

The first law of optics is: 1/OD + 1/ID = 1/FL .

Therefore, if you take a lens at infinity focus, the Object Distance (OD), must be at infinity (generally, that's assumed to be 1000*FL of the optic), and the Image Distance (ID) is going to be 1*FL away from the center of the optic.

As you get closer to the Object, the Image Distance increases, and thus, for a 50mm lens, if we focus at 5000 mm (5 meters), the ID is 50.505050505050...

You can play with this formula at https://mathsolver.microsoft.com/ It'll open your eyes to a lot of reasons why that lens won't focus closer than 1/1000 *FL.

 

[Don H Marks]

Another good rule of thumb is that one can't make a focused image if the subject and film are less than 4 focal lengths apart.