Magnification; What's focal point

[CuteWolf]

After using the equation 1f = 1÷d_o + 1÷d_i I found what the focal point / f was.
Now, what would the focal point represent? Is the focal point the image height or object height in the equation m = h_i÷h_o = -d_i÷d_o

 

[Andy Resnick]

'f' is not a point; 'f' is the focal *distance*. It is the distance from the lens, if plane parallel light were incident on the lens, at which the light would focus to a point.

The magnification of the system is given by the *ratio* of front and back focal lengths (which is equivalent to the ratio of image distance to object distance).

In most optical systems, the focal point (or focal plane) is not a real surface. When designing an optical system, it's often helpful to keep track of the focal planes/lengths, because then it's straightforward to add or modify lenses to get a desired result- a certain magnification, for example.

 

[schip666!]

Slight amplification: the focal length of a lens is the distance from the lens where incident light from a point-source "object" at infinity (who's "rays" are effectively parallel) will be focused into a point "image". You can use that length to calculate (with the formula you gave) the relative distances of object and image for any other combination. The magnification is then the ratio of those two distances.