Reflection by spherical mirrors

Sign convention (the Cartesian one): measure every distance from the pole P of the mirror.

• Distances in the direction the incident light travels are positive; against it, negative.
• Heights above the axis are positive, below negative.

With light coming from the left, the object distance u is always negative.

So a concave mirror has a negative focal length and a convex mirror a positive one. For both, f = R/2.

Mirror equation: 1/v + 1/u = 1/f. Magnification: m = h′/h = –v/u.

Read the answer by its sign:

• v negative: the image is in front of the mirror, real, and inverted (m negative).
• v positive: the image is behind the mirror, virtual, and erect (m positive).
• |m| > 1: bigger than the object; |m| < 1: smaller.

Example: concave mirror, f = –10 cm, object at u = –30 cm. 1/v = –1/10 + 1/30 = –2/30, so v = –15 cm. m = –(–15)/(–30) = –0.5: real, inverted, half the size.

Example: convex mirror, f = +20 cm, object at u = –20 cm. 1/v = 1/20 + 1/20, so v = +10 cm. m = +0.5: virtual, erect, smaller.

A convex mirror always gives a virtual, erect, smaller image, whatever the object distance. Its wide view is why it is used as a rear-view mirror.

Always put the signs into the formula with the numbers; never change the formula itself.