Focal length

Printed on the AP Physics 2 sheet, and it serves mirrors and lenses alike. The sign of $f$ is what tells the equation which optic you have.

One pattern generates the table: $f$ is positive when real light actually converges at the focal point, and negative when the rays only appear to come from it. A concave mirror can start a fire, a convex one cannot.

Focal point and focal length are not the same thing. The focal point is a place, where rays parallel to the principal axis meet or appear to meet. The focal length is a signed distance to it. A lens has a focal point on each side; for the thin symmetric lenses this course uses, both sit $|f|$ from the centre, so one number describes the lens.

For a spherical mirror the CED says the focal point may be approximated as the point halfway between the surface and the centre of curvature, so $|f| = R/2$ for rays close to the axis. That relation is not on the equation sheet, so halve the radius yourself. No equivalent exists for lenses: no lensmaker's equation appears anywhere in AP Physics 2, so a lens focal length is given or measured. A flat mirror has infinite $f$, and $1/f = 0$.