Scholars and the plane mirror

In a plane mirror the image of an object is virtual (not real — the extensions of the rays meet), upright and the same size as the object; it forms behind the mirror at the same distance as the object is in front, and left and right are swapped. To construct the image, draw two rays from a point of the object; the point where the extensions of their reflected rays meet is the image. If the mirror is turned through an angle α, the reflected ray turns through 2α. Spherical mirrors are parts of a sphere: a concave mirror gathers rays at a focus (projectors, headlights, dentist’s mirror), a convex mirror scatters them and gives a small, upright, virtual image — which is why a car’s rear-view mirror has a wide field of view. For concave and convex mirrors: 1/d + 1/f = 1/F, where d is the object’s distance from the mirror, f the image’s distance, F the focal length. For example, with F = 20 cm and f = 30 cm, 1/d = 1/20 − 1/30 = 1/60, so d = 60 cm.