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FAQ: Focal length, field of view and formats


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#1 Laurent Andrieux

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Posted 25 February 2005 - 08:24 AM

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
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#2 Aaron Solomon

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Posted 13 September 2010 - 04:44 PM

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.
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#3 Simon Wyss

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Posted 06 November 2010 - 06:08 AM

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.
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#4 Brian Drysdale

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Posted 06 November 2010 - 11:57 AM

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.
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