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Old January 19th, 2010, 11:50 AM
Doug Kerr Doug Kerr is offline
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Default Effective focal length

I'm going to talk a little about "effective focal length", and not in the way you are probably expecting.

We are all familiar with the convention in which we describe the field of view to be given by a lens of a particular focal length, used on a camera with a particular format size, by essentially answering this question:

"What focal length lens, used on a camera with a 36 mm x 24 mm format, would yield the same field of view that this lens yields on this camera?"

That number may be reasonably called the "full-frame 35-mm equivalent focal length" of the lens of interest used on the camera of interest. Like all reasonable names, it of course does not explain the whole concept - we must have some awareness of the concept before we go fooling around with it.

I'll mention in passing that "full-frame 35-mm" is a fairly accurate and complete way to describe cameras with a format size of 36 mm x 24 mm. "Full-frame" by itself doesn't do it (that term actually refers to the largest normal frame size used with a certain film size; for "8x10" film, the full frame format is very nearly 8" x 10"). "35-mm" by itself doesn't do it; there were numerous cameras using 35-mm film ("type 135" film, to be really precise) whose format size was 18 mm x 24 mm (the "half-frame 35-mm" cameras).

Now "effective focal length" (which we sometimes hear) is not a good shorthand, if for no other reason that the one I will discuss shortly.

Note again just for completeness that the "full-frame 35-mm equivalent focal length" is not in any way "a focal length" of the lens. The focal length of a lens (for zoom lenses, assuming a certain zoom setting, and in any case, perhaps assuming a certain focus setting) is a fundamental optical property of the lens. It has it regardless of what camera it might be on, if any. It has it when in your sock drawer. And it is not defined in a way that has anything to do with format size. (We sometimes hear, "The reason we need to use a focal length factor is that the focal lengths of lenses are stated in '35-mm camera' terms". Not so at all.)

But helping is to get, or remain, confused in this area is that, in techncial papers and optical textbooks, we see reference to the effective focal length of a lens. What is that?

It is just the focal length of the lens, as I have discussed above. So why the "effective"?

To understand this, we have to go back a little in the history of optics. Initially what was noticed was that if we have an "object" at infinity, its image was formed a certain distance behind the lens - that it, behind its "rear vertex", the face of its rearmost element. That distance was called the "focal distance", or even, "focal length", of the lens.

For thoroughness, some of these workers did the same thing in reverse, putting a test object "at infinity" behind the lens, and allowing an image to be formed in front.

Then, of course, to keep things straight, they began to refer to the "front focal distance" and "back focal distance", or perhaps "front and back focal length".

Now, as the understanding of optical systems grew, the workers realized that, for any lens (even a "thick" one, or a compound lens composed of several elements), there was a critical parameter that affected such things as the magnification of the lens in a certain situation and how the object and image distance were related. In the classical case, of a test object in front of the lens at infinity, forming an image behind the lens, that was the distance to the image, but not measured from the rear vertex, but rather from some "abstract" point inside the lens.

Since it was this "length" that was a parameter of all the emerging equations, and governed many optical properties of the lens "in place", it was decided to call it the "effective focal length". And that notation is in use today in formal optical textbooks and papers.

But remember, this is just the "focal length" of which we normally speak.
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Old January 19th, 2010, 12:06 PM
StuartRae StuartRae is offline
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Default

Quote:
.......if we have an "object" at infinity.........
That reminds me of our old physics teacher at school. Someone once asked him "Sir, where is infinity?", to which he replied "Gentlemen, for the purpose of this experiment infinity is at the end of my desk".

Regards,

Stuart
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