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Physics · Glossary

What is Magnification?

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

The magnification of the image is

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

∣γ∣\abs{\gamma} compares sizes, its sign orientations (γ<0\gamma < 0: inverted); the sign of OA′‾\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 cm30\,\mathrm{cm} in front of a converging lens with f′=10 cmf' = 10\,\mathrm{cm}: OA‾=−30 cm\overline{OA} = -30\,\mathrm{cm}, so

1OA′‾=110−130=115,OA′‾=+15 cm,γ=15−30=−0.50:\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 cm15\,\mathrm{cm} behind the lens, inverted, half-size — exactly what the three rays draw.

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