Images by Rays

Virtual Image Back-Trace

object inside the focus

When the object is inside the focal length, the outgoing rays spread out and their back-projections meet at an upright virtual image.

Example

When the object is inside the focal length, the outgoing rays spread out and their back-projections meet at an upright virtual image. 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 inside the focus

The object distance is only 5 metres, inside the focal length. The outgoing rays spread out instead of meeting on the far side.

u=5 mu = 5\ \text{m}
A virtual lens imageOutgoing rays spread; back-projections meet.FFlensobjectimage

Trace the rays backward

The dashed back-projections meet on the object side of the lens. The signed image distance is -10 metres, and the magnification is 2, so the virtual image is upright and 8 metres tall.

v=−10 mm=2himage=8 mv = -10\ \text{m}\qquad m = 2\qquad h_{\text{image}} = 8\ \text{m}
A virtual lens imageOutgoing rays spread; back-projections meet.FFlensobjectimage

Inside the focus flips the image-distance sign

Compare one outside-focus row with two inside-focus rows. Once the object is inside the focus, the image distance is negative and the magnification is positive.

fuvm10 m20 m20 m−110 m5 m−10 m210 m4 m−203 m53\begin{array}{c|c|c|c}f&u&v&m\\10\ \text{m}&20\ \text{m}&20\ \text{m}&-1\\10\ \text{m}&5\ \text{m}&-10\ \text{m}&2\\10\ \text{m}&4\ \text{m}&\tfrac{-20}{3}\ \text{m}&\tfrac{5}{3}\\\end{array}
A virtual lens imageThe middle table row is this checked back-trace case.FFlensobjectimage
optics Dashed back-projections show where the rays appear to come from; the outgoing rays do not pass through the virtual image.