11.1 Linear magnification

Linear magnification compares image length with object length: M = image length / object length. Use matching dimensions, such as height with height, and use the same units in numerator and denominator. The units cancel, so magnification has no unit.

If M > 1, the image is larger than the object. If M = 1, it is the same size. If 0 < M < 1, it is diminished. The syllabus treats magnification as a positive size ratio; image orientation is stated separately rather than represented by a negative sign.

11.2 Measuring from diagrams

In a scale ray diagram, object and image heights can be measured with a ruler. The calculated ratio should agree with the visible size change. The drawing must be sufficiently large and the image arrow endpoints clearly defined.

If the diagram is not stated to be to scale, do not measure it for a numerical answer. Use data given in the question. Always check whether values are in mm, cm or another unit before forming the ratio.

11.3 Rearranging the equation

Image length = M × object length. Object length = image length / M. Rearrangement is straightforward but interpretation matters. For example, M = 2.4 means every linear dimension of the image is 2.4 times the corresponding object dimension.

Linear magnification does not directly give area magnification. If both dimensions are enlarged by a factor of 2, the area is enlarged by a factor of 4. Area magnification is beyond the requirement unless explicitly developed in a question.

11.4 Magnifying glass

A magnifying glass is a converging lens with the object placed inside the focal length. Rays emerging from the lens diverge, and the eye traces them backward to a virtual, upright and enlarged image. The image is on the same side of the lens as the object.

Moving the object closer to F generally increases the apparent image distance and magnification, but focusing becomes sensitive. The observer adjusts lens–object and eye–lens distances until the image is clear. A magnifying glass does not create a real enlarged image on a screen in normal use.

11.5 Distinguishing magnification from resolution

Magnification makes an image larger; resolution is the ability to distinguish fine detail. Enlarging a blurred or low-resolution image does not reveal unlimited new information. A good optical system must form a sharp image as well as provide suitable magnification.

At O Level, questions usually focus on the size ratio and ray diagram. However, using accurate terms helps avoid claims that a magnifying glass “makes the object larger”; it forms a larger apparent image.

Worked examples

Practical focus

Examination guidance

Check your understanding

1. An object is 12 mm high and its image is 30 mm high. Find M.
2. What does M = 0.4 mean?
3. Why can the magnifying-glass image not be projected?