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 Imaging Technology: Theory, Alternatives, Practice and Advances. This is a brand independent discussion of theory, process or device. Ignore this forum unless this matters to you!

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October 28th, 2010, 09:31 AM
 Doug Kerr Senior Member Join Date: May 2006 Location: Alamogordo, New Mexico, USA Posts: 8,625
Effective focal length

The focal length that we know and love (and which appears frequently in equations in technical articles) is formally called effective focal length.

This makes it sound as if there is a (different) real focal length, and the number we use is somehow adjusted from that to take some situation into account (just as we have in the effective f-number that pertains to camera exposure for nearby objects).

But in fact not - the "effective focal length" is the real focal length of the lens. It got that name as a result of historical development.

When lens behavior was first studied, it became apparent that if we had a well-behaved lens regard a very distant object ("at infinity"), an image of that object was formed behind the lens. The distance to that image varied with the surface curvature of the lens, and so it was clearly an important parameter of the lens.

The location of this image was said to be the rear focal point of the lens, and the distance to it was measured from the rearmost point of the lens (on the axis) - the rear vertex of the lens. This distance was called the "back focal distance", or "back focal length", of the lens. We encounter it today in discussions of lens designs, such as when discussing the defining properties of the Canon EF-S series lenses.

But soon it was realized that the number that affected many properties of the lens (and thus that was needed in many equations about lens behavior) was not the back focal length, but rather a slightly greater (in most cases) distance. Not surprisingly, this came to be called the "effective focal length".

This was in fact the distance to the rear focal point from a place (usually) inside the lens called the rear principal plane. That's not something we can see, nor locate in any simple way, so it was understandable that the effective focal length remained an ethereal, if theoretically important, distance, and in formal writing, the designation effective focal length continued in use to denote it.

Nevertheless, this distance is the "real" focal length of the lens - the only number that is of importance in such things as focus equations, field of view reckoning, and so forth. If we put aside zoom lenses and lenses that focus by moving just some of the elements, it is a constant for the lens, not dependent on any "circumstance" of the photographic setup.

Optometric work

In optometric work (related to vision correction - "eyeglasses"), we generally speak not of the focal length of a lens but rather its (refractive) power, which is defined as the reciprocal of the focal length.

For various reasons, the power "rating" of eyeglass lenses is not the reciprocal of the effective (real) focal length but rather the reciprocal of the back focal length. (The theory behind this is very convoluted.)

The people who formulated this notion were so proud of its importance that they chose to call the power defined in this way (rather from the effective focal length) the "effective power" of the lens!

The power defined this way - the reciprocal of the back focal length, measured from the rear vertex of the lens - is called the vertex power of the lens. One trademark name of a focimeter - an instrument used to determine the power of an eyeglass lens - is "Vertometer", based on that. (You will perhaps see our newly-acquired vintage Vertometer later today.)

Best regards,

Doug

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