What is Spherical mirror? — Physics

Definition 3.5 University Physics — Year 1 · Chapter 3 — Mirrors and Thin Lenses

A spherical mirror is a reflecting spherical cap of center $C$ and vertex $S$ (its intersection with the axis). It is concave if the light meets the hollow side ( $C$ on the side of the incoming light), convex otherwise. Its focus $F$ is the image of a point at infinity on the axis; its focal length is $f = \overline{SF}$ .

A concave mirror (C, focus F at mid-radius). For an object AB beyond C, the ray parallel to the axis returns through F and the ray through F returns parallel: they cross at B' — a real, inverted, reduced image between F and C. — A concave mirror ( $C$ , focus $F$ at mid-radius). For an object $AB$ beyond $C$ , the ray parallel to the axis returns through $F$ and the ray through $F$ returns parallel: they cross at $B'$ — a real, inverted, reduced image between $F$ and $C$ .

Examples

Example 3.9 (Shaving mirror, rear-view mirror)

A concave mirror of radius $60\,\mathrm{cm}$ ( $f = -30\,\mathrm{cm}$ ) with a face at $20\,\mathrm{cm}$ : $1/\overline{SA'} = -1/30 + 1/20 = 1/60$ , $\overline{SA'} = +60\,\mathrm{cm}$ — behind the mirror, virtual — and $\gamma = -60/(-20) = +3$ : upright, three times larger, the shaving mirror. A convex mirror of radius $2.0\,\mathrm{m}$ ( $f = +1.0\,\mathrm{m}$ ) with a car $20\,\mathrm{m}$ behind: $1/\overline{SA'} = 1 + 1/20$ , $\overline{SA'} = 0.95\,\mathrm{m}$ (virtual, behind), $\gamma = +0.048$ : upright, twenty times smaller, and therefore a wide field — the rear-view mirror, with its warning that objects are closer than they appear.

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Examples

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