One of the basic laws of optics is
the thin lens formula. But for
some reason Wikipedia hides it in a different page
(Lens (optics)). The information
there is correct, but I don't like the way it's presented.
In particular, to quote Wikipedia (as of 2 December 2017),
If the distances from the object to the lens and from the lens to the image are S₁ and S₂
respectively, for a lens of negligible thickness, in air, the distances are related by the
thin lens formula
It notes elsehwhere that f is
the focal length of the lens. But
why S₁ and S₂? I've learnt u and v, and the difference is
imprinted in my mind. S₁ and S₂ look like subscripts, which they're not (the
term S₂ is meaningless, for example). So on my pages I refer to u (subject
distance) and v (object distance, from centre of lens
to focal plane (sensor or film, for
example).
There are a few other things of interest about this formula:

The formula applies to “thin lenses”. No lens is has zero thickness, but something like
a magnifying glass is close enough. It doesn't apply exactly for other lenses, in
particular camera lenses, but it's the best that we have without better understanding of
the lens construction.

As the Wikipedia variable names suggest, u and v are symmetrical.

The minimum value of u + v is when they're both the same, and in
this case the formula makes it clear that they are each 2f. So the closest
distance between subject and focal plane is 4f.