Magnification Calculations

Magnification tells you how many times larger (or smaller) the image is compared to the object.

$m = \frac{\text{image height}}{\text{object height}} = \frac{v}{u}$

where $v$ is the image distance from the lens and $u$ is the object distance from the lens.

Interpreting magnification

• $m > 1$: image is magnified (larger than the object).
• $m = 1$: image is the same size as the object.
• $m < 1$: image is diminished (smaller than the object).

Worked example

An object 3 cm tall is placed 20 cm from a converging lens. The image is 12 cm tall.

$m = \frac{12}{3} = 4$

The image is 4 times the height of the object.

Using the thin lens equation (Supplement)

$\frac{1}{f} = \frac{1}{u} + \frac{1}{v}$

Example: Object distance $u = 15$ cm, focal length $f = 10$ cm.

$\frac{1}{v} = \frac{1}{10} - \frac{1}{15} = \frac{3 - 2}{30} = \frac{1}{30}$

$v = 30 \text{ cm}$

$m = \frac{v}{u} = \frac{30}{15} = 2$

The image is twice the height of the object.

Common errors and how to correct them

• Confusing magnification with actual image size. $m = 4$ means the image is 4 times the object height, not 4 cm.
• Forgetting that magnification is a ratio (no units).

How to apply this in an exam

Use $m = \text{image height}/\text{object height}$ or $m = v/u$. Show the substitution and state whether the image is magnified or diminished.