Focal Length - John Dunn, Consultant, Ambertec, P.E, P.C.

The following simplified sketch illustrates the concept of the "focal length" of a convex lens. Emissions from a light source located at one distance, call that "d1", will come to a focal point on the other side of the lens at the distance called "d2" and vice versa as well. 

If, as we go from the left side sketch to the right side, we allow "d1" to get larger and larger without limit, if we let "d1" go to infinity, then the distance "d2" approaches the focal length of the lens. This is often called "focus at infinity."

That phrase, "focus at infinity", once got somebody whom I know very well, somebody who is actually quite a good photographer, very upset because obviously nothing can be located at infinity so clearly that phrase can't possibly have any real meaning and I had to be wrong in trying to say it does.

No matter what, I simply could not break the impasse against grasping this concept. ( It was another preconception issue. )

It is interesting to note that the flatter the curvature is made, the longer the focal length becomes. For a perfectly flat window pane, the value of the focal length goes to infinity.

Comments

[John Dunn]

Clearly (pun intended), this is a simplification of the topic. For a nice write-up in greater detail, take a look at:

http://en.wikipedia.org/wiki/Focal_length

[George Storm]

As you say - somewhat simplified.
Your photographer friend would have been on firmer ground if he had contested the equation: 1/u+1/v=1/f
For real (thick and/or multi-element) lenses the reference plane is not stationary and the magnification does not correspond to a constant focal length.

[William Ketel]

The fact is that as a number gets vary large, it's reciprocal does get very small, and if we are using fixed-point arithmetic the vary small number may indeed drop out, equivalent to becoming zero. So while a lens may not be focused on actual infinity, it can be focused on some point far enough away so that the difference is not measurable with common measurement procedures. In short terms, "close enough" to infinity.