Images by Rays

Real Image Intersection

rays meet on the far side

When the object is beyond the focal length, the principal rays can meet on the far side of the lens to form a real inverted image.

Example

When the object is beyond the focal length, the principal rays can meet on the far side of the lens to form a real inverted 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 beyond the focus

The object distance is 20 metres, while the focal length is 10 metres. The object is beyond the focus, so the principal rays can meet on the far side of the lens.

u=20 mf=10 mu = 20\ \text{m}\qquad f = 10\ \text{m}
A real lens imagePrincipal rays meet on the far side of the lens.FFlensobjectimage

The rays meet on the far side

The checked ray intersection gives an image distance of 20 metres. The signed image height is -4 metres; the negative sign means the image is inverted.

v=20 mhimage=−4 mv = 20\ \text{m}\qquad h_{\text{image}} = -4\ \text{m}
A real lens imagePrincipal rays meet on the far side of the lens.FFlensobjectimage

Real image distance grows as the object nears focus

With the focal length fixed at 10 metres, compare three object distances outside the focus. The closer object gives the farther, taller real 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}
A real lens imageThe middle table row is this checked ray case.FFlensobjectimage
optics The real image is where the drawn rays actually meet. Its downward arrow means the magnification is negative.