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When you look into a bathroom mirror, how does the size of the image you see of your head ‘on’ the mirror compare with the true size of your head? Make a prediction!

You may need a partner to help you test your answer. (You might substitute a paper or balloon ‘head’ for yours and mount it at the same distance you would be if you were looking in the mirror.)

Measure the actual width (1) and height (2) of your head in cm, and record them.

Using tape or a water-soluble ink pen, mark the top and bottom and sides of your head right on the mirror.

Measure the dimensions (3) and (4) of your head as seen ‘on’ the mirror. Record the measurements.

How do the two sets of dimensions compare? Are you surprised? What happens if you stand twice as far from the mirror?

“What gives?”

Why does your image in a mirror appear to measure half the size of your face?

Imagine a ray of light TM coming from the top of your head at T, and reflecting at M to your eye at E. Imagine another ray of light BN coming from the bottom of your head at B and reflecting at N to your eye at E. To your eye, these rays will appear to have come from T’ and B’ on the virtual image T’B’.

If you put tape on the mirror and measure the size of the image, you will be measuring (in one dimension) MN. However, the virtual image T’B’ is the same size as the object TB.

Assuming a perfect mirror (no thick glass), triangle EMN is half the size of triangle ET’B’, therefore MN is half the width of T’B’ or TB. What you measure (MN) will be half the height of either the object or the virtual image.

At different distances, the ‘triangles’ would become lengthened, but the same geometry would hold true.