Lenses & Imaging
A lens redirects many rays from each object point. Where those rays converge—or appear to diverge from—determines the image position, orientation, and size.
How can curved glass create an image somewhere else in space?
Each small region of the lens refracts light. The lens shape organizes those direction changes so rays from one object point either meet again or leave with directions that appear to come from a common point.
This page uses a converging thin lens and the usual real-is-positive sign convention for image distance.
Move the object through the focal region.
For a converging lens with dₒ > f, outgoing rays can actually meet on the far side, producing a real inverted image.
When dₒ < f, outgoing rays diverge. Tracing them backward produces an upright virtual image on the object side—the magnifying-glass regime.
The familiar parallel, focal, and central rays are selected representatives of a much larger family of refracted rays from the same object point.
The outgoing rays are parallel in the ideal thin-lens model, so the image is described as being at infinity.
Negative magnification means the image is inverted relative to the object; positive magnification means upright.
Light paths through passive optical systems are reversible, so object and image roles can often be exchanged geometrically.