Farther Image, Taller Image - Optics Step by Step

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

optics All distances are schematic clean metre distances so the ray geometry remains exact and inspectable.

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\ \text{m}

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\ \text{m}\qquad m = -2\qquad h_{\text{image}} = -8\ \text{m}

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.

\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}