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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
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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:

  1. 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.
  2. As the Wikipedia variable names suggest, u and v are symmetrical.
  3. 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.

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