What is Magnification? — Physics

Definition 10.9 High School Physics · Chapter 10 — Lenses, Images, and the Eye

The magnification of the image is

\gamma = \frac{\overline{A'B'}}{\overline{AB}} = \frac{\overline{OA'}}{\overline{OA}} .

$\abs{\gamma}$ compares sizes, its sign orientations ( $\gamma < 0$ : inverted); the sign of $\overline{OA'}$ reads the nature (positive: real, behind the lens; negative: virtual, in front).

Examples

Example 10.10 (The formula at work)

An object stands $30\,\mathrm{cm}$ in front of a converging lens with $f' = 10\,\mathrm{cm}$ : $\overline{OA} = -30\,\mathrm{cm}$ , so

\frac{1}{\overline{OA'}} = \frac{1}{10} - \frac{1}{30} = \frac{1}{15}, \qquad \overline{OA'} = +15\,\mathrm{cm}, \qquad \gamma = \frac{15}{-30} = -0.50 :

a real image $15\,\mathrm{cm}$ behind the lens, inverted, half-size — exactly what the three rays draw.

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Examples

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