Images by Rays

Farther Image, Taller Image

moving inside two focal lengths

Moving the object closer to the focal point pushes the real image farther away and makes it taller.

Example

Moving the object closer to the focal point pushes the real image farther away and makes it taller. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Move the object closer to the focus

Now the object distance is 15 metres. That is still outside the focus, but closer than the same-size case, so the image lands farther away.

u=15 mu = 15\ \text{m}
A taller real imageThe real image is farther away and inverted.FFlensobjectimage

The image is farther and taller

The checked image distance is 30 metres. The signed magnification is -2, so the image height is -8 metres: inverted and twice as tall.

v=30 mm=−2himage=−8 mv = 30\ \text{m}\qquad m = -2\qquad h_{\text{image}} = -8\ \text{m}
A taller real imageThe real image is farther away and inverted.FFlensobjectimage

Closer real objects make larger inverted images

The table keeps the focal length fixed and moves the object toward the focus. The magnitude of the negative magnification grows from one half to twice size.

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}
A taller real imageThe last table row is this checked ray case.FFlensobjectimage
optics All distances are schematic clean metre distances so the ray geometry remains exact and inspectable.