Lens Equation and Magnification

Same Size Case

object at twice the focus

When the object is two focal lengths from a converging lens, the real image is the same size and inverted.

Example

When the object is two focal lengths from a converging lens, the real image is the same size and inverted. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Put the object at twice the focus

With focal length 10 metres, put the object at 20 metres. That is the clean same-size setup.

u=20 mf=10 mu = 20\ \text{m}\qquad f = 10\ \text{m}
Same-size real imageObject and image distances match.FFlensobjectimage

Compare the same-size row with nearby rows

Keep the focal length at 10 metres. Farther than twice the focus makes a smaller image; closer than twice the focus makes a larger image.

fuvm10 m30 m15 m−1210 m20 m20 m−110 m15 m30 m−2\begin{array}{c|c|c|c}f&u&v&m\\10\ \text{m}&30\ \text{m}&15\ \text{m}&\tfrac{-1}{2}\\10\ \text{m}&20\ \text{m}&20\ \text{m}&-1\\10\ \text{m}&15\ \text{m}&30\ \text{m}&-2\\\end{array}
Same-size real imageThe middle table row is the checked same-size ray case.FFlensobjectimage

Distance matches, size matches

The checked image distance is also 20 metres. The magnification is -1: same size, but inverted.

v=20 mm=−1v = 20\ \text{m}\qquad m = -1
Same-size real imageObject and image distances match.FFlensobjectimage
optics This is the clean benchmark case: equal object and image distances with magnification minus one.