Diverging lens

Known equally as a concave lens. The CED says its refracted rays "diverge as if they originated from a focal point on the incident side", and the words "as if" are doing the work: nothing is really there.

Negative focal length, because that focal point sits on the side the light came from, which the sign convention makes the negative side.

One behaviour, no cases. For any real object, at any distance, the image is virtual, upright, reduced, and on the same side as the object. One line proves it rather than six rows of a table: with $f$ negative,

is a negative number minus a positive one, so $1/s_i$ is negative for every positive $s_o$, and $s_i$ is always negative. The same expression makes $|1/s_i|$ larger than $1/s_o$, so $|s_i| < s_o$ and the magnification magnitude is always below 1.

That predictability is why it turns up as the easy case on exams: you can answer the type, orientation and relative size before touching a calculator.

What makes it the opposite of a [converging lens](/glossary/converging-lens): it spreads a parallel bundle instead of gathering it, so no real image and no burning point are available to it at all. It also behaves like a convex mirror, because diverging is diverging whichever way the light travels.