# Imaging through lenses

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## Lens types

### Converging lens

Because of the lens grinding equation, the focal length depends $f$ a lens from the radii $r1,r2$ of the two spherical surfaces, whereby the sign convention for refraction must be observed. With a positive focal length $f$ it is a converging lens, which owes its name to the ability to collect parallel incident rays in its focal plane (see above illustration and photo). The focal plane is the area that contains the focal point and is perpendicular to the optical axis. By concentrating the energy of the parallel rays in one point (which would otherwise have been distributed over a larger area), you can set flammable material on fire if you hold it at this distance in front of the lens - hence the name focal point. Because of the reversibility of the beam path, all rays that pass through the focal point are parallel behind the lens axis. In general, it applies to the converging lens that parallel rays unite in one point in the focal plane. We will use this property later for the image construction with a converging lens. Provided $nlens>nair$ the focal length and thus the refractive power becomes positive if the lens is thicker in the center than on the outside.

### Diverging lens

If the focal length of a lens is negative, then there is a diverging lens. With such a lens, light rays cannot be focused; it only generates virtual images. If rays fall on the lens parallel to the optical axis as shown above, they appear to an observer behind the lens after refraction$F´$ get. Parallel rays incident at any angle appear to come from a common point which is located in the object-side focal plane after imaging through the lens. In contrast to the converging lens, the diverging lens has a virtual point of origin of the same instead of a real union of the parallel rays.