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I thought this was a simple question but can't seem to find a direct answer.

In ray diagrams with a converging or diverging lens, we always draw F (the focal length) on both sides of the lens. But the focal point for any thin lens is only one, isn't that right? The point at which light converges or appears to converge.

Or is it two, depending on different situations... such as objects placed behind or in front of the lens?

What do we officially say? Does a lens have two foci or one?

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    $\begingroup$ This is really a question of semantics not physics. A lens has a focal length, and it can work in both directions because it is symmetric. $\endgroup$ – Chris Mueller Mar 1 '15 at 15:27
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    $\begingroup$ A lens has two distinct foci if it's asymmetric! A singular focal length of a lens is given when it is symmetric. Even then, the fact remains that a lens has two focal points - one on each side. $\endgroup$ – Nick Mar 7 '15 at 7:20
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A lens is symmetric. By this I mean you can pick it up, turn it round and put it back and the light rays don't change. Or to look at it another way, it doesn't matter whether the light travels from left to right through the lens or right to left.

So parallel light travelling from infinity on the left of the lens will converge at the focal point on the right. Likewise parallel light travelling from the right of the lens will converge at the focal point on the left.

Lens

So in this sense a lens has two focal points - one on each side.

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  • $\begingroup$ Yes - but note that "real" lenses need not be symmetric, and are optimized for a particular direction (eg Plano convex lens). These may not have a focal "point" in one direction because of spherical aberration that is eliminated in the other direction. $\endgroup$ – Floris Mar 1 '15 at 21:50

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