Reflection of Light at Curved Surfaces
Curved mirrors are portions of hollow spheres. The AP paper asks you to draw ray diagrams, apply the mirror formula with correct signs, and explain the uses of concave and convex mirrors.
Vocabulary and sign convention
- Pole (P), centre of curvature (C), principal axis, principal focus (F), and focal length f = R/2.
- Distances are measured from the pole; those measured along the direction of incident light are positive, so u is negative for a real object placed in front of the mirror.
- Heights above the principal axis are positive, below it negative.
- A concave mirror has a real focus (f negative in this convention); a convex mirror has a virtual focus (f positive).
Rules for ray diagrams
A ray parallel to the axis passes through F after reflection; a ray through F emerges parallel to the axis; a ray through C retraces its path; a ray striking the pole reflects at an equal angle on the other side of the axis.
Worked example
An object stands 20 cm in front of a concave mirror of focal length 15 cm. With u = −20 cm and f = −15 cm: 1/v = 1/f − 1/u = (−1/15) − (−1/20) = (−4 + 3)/60 = −1/60, so v = −60 cm. The image is real, inverted, 60 cm in front of the mirror, and m = −v/u = −(−60)/(−20) = −3, that is, three times larger than the object.
Traps
- For a convex mirror u is negative but f and v are positive; the image is always virtual, erect, diminished and behind the mirror.
- A negative magnification means an inverted image; |m| greater than 1 means enlarged.
- Do not write f = R; the correct relation is f = R/2.
- A plane mirror is the limiting case as R tends to infinity.
Uses: concave mirrors in torches, shaving mirrors, solar cookers and dentist mirrors; convex mirrors as rear-view and security mirrors because they give a wide field of view.