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Lesson: Chapter 5 — Optics

5.2. Curved (spherical) mirrors 4 of 4

Focus and focal length

A ray along the principal axis has an angle of incidence of zero, so it reflects straight back along the axis. Rays parallel to the axis do something more useful.

Concave: the rays meet

A parallel beam reflected by a concave mirror, every ray passing through the focus F.

Rays parallel to the axis all pass through one point on the axis after reflection. A screen there would show a very bright small spot. That point, F, is the focus.

Convex: the rays spread

A parallel beam reflected by a convex mirror, spreading out; traced back, dashed, the rays seem to come from the focus F behind the mirror.

After a convex mirror the reflected rays spread out, and seem to come from a point F behind the mirror: its focus.

Focal length and radius of curvature

The focus lies midway between the pole and the centre of curvature. The distance from the pole to the focus is the focal length (f); from the pole to the centre of curvature, the radius of curvature (r).

Radius of curvature

r = 2f

the radius of curvature is exactly twice the focal length