Magnification

Magnification is a measure of the size of an image compared to the size of the object. Lenses and curved mirrors can produce magnified images.

Calculating magnification

The magnification produced by a lens can be calculated using the equation:

magnification = \frac{image~height}{object~height}

Magnification is a ratio of two lengths, so it has no units. However, the image height and object height should both be measured in the same units, eg centimetres (cm) or millimetres (mm), but not a mixture of the two.

Example 1

An object that is 2 cm tall forms an image 250 cm tall. Calculate the magnification.

magnification = \frac{image~height}{object~height}

magnification = 250 \div 2

magnification = 125~(magnified)

Example 2

An object 1.8 m tall forms an image 1.8 cm tall. Calculate the magnification.

First convert metres to centimetres: 1.8 × 100 = 180 cm

magnification = \frac{image~height}{object~height}

magnification = 1.8 \div 180

magnification = 0.01~(diminished)

Question

An object 3 mm tall forms an image 12 mm tall. Calculate the magnification.

magnification = 12 ÷ 3

magnification = 4