Focal Length - Optics Step by Step

The focal length is the distance from the lens to its focal point. It sets the scale for the ray diagram.

optics Clean metre distances are schematic model distances chosen for exact geometry, not realistic lens hardware sizes.

Example

The focal length is the distance from the lens to its focal point. It sets the scale for the ray diagram. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

A lens has focal marks

The focal point is measured along the axis from the center of the lens. In this clean diagram, that distance is 10 metres.

f = 10\ \text{m}

Changing focal length moves the focus

The focal length is the distance from the lens to the focus. The diagram shows the middle row; the table shows how changing the focal length changes that mark.

\begin{array}{c|c}f&\text{focus distance}\\6\ \text{m}&6\ \text{m}\\10\ \text{m}&10\ \text{m}\\14\ \text{m}&14\ \text{m}\\\end{array}

The focal length sets the diagram scale

Once the focal length is fixed, the principal-ray rules know where to aim. Parallel rays bend through a point one focal length from the lens.

\text{parallel ray} \rightarrow \text{focus at } f