There are hundreds of patented designs for camera lenses. Although it would be absurd to attempt to discuss them all, it is quite reasonable to categorize them into a fairly small number of camera lens types. The list below gives the types, roughly in order of their introduction. Lenses made of crown glass, with low dispersion, are shown in cyan and lenses made of flint glass, with high dispersion, are shown in magenta. In the lenses where the aperture stop is separated from the lens elements, it is shown as an inverted “T” above an upright one.
This is the original camera lens type. It consists of a positive meniscus lens and a stop. Performance is not great, with 10°-20° half angles at f/8 to f/16. The best part is that the lens is simple and inexpensive. It was used on all of the simple Kodak cameras in the early 1900’s but in a form where the lens is to the left of the stop.
The Petzval lens was invented to provide a reasonably fast f/# to make it possible to take pictures with the relatively insensitive photographic film of the late 1800’s. An f/2 lens with a 10° field of view is realistic.
This form, developed in the last decade of the 1800’s has three separated elements, making it possible to correct axial and chromatic aberration as well as spherical aberration, coma and astigmatism, to an impressive extent. This example covers 20° at f/4.
Although it looks like a Cooke triplet in which the last lens is replaced by an achromatic doublet, the invention came about in a very different way. Paul Rudolph, the inventor, started with a pair of achromatic doublets and separated the first one to get more design freedom. Performance is only slightly better than a Cooke triplet; this lens covers 24° at f/4.
Friedrich Gauss invented a telescope objective that, due to its strong curvatures, was not very practical. However, when two of them are placed symmetrically about a stop, an excellent photographic objective is obtained. Later designers turned the two middle lenses into achromatic doublets, as is shown here. This lens covers 24° at f/2.8, a full stop faster than the Tessar, allowing exposures to be only half as long.
A major problem with long focal length lenses is that the lens needs to be held a long way from the camera body. A telephoto lens reduces this problem by following a positive first element or group with a negative one. This makes the effective focal length of the lens much longer than the lens itself. This very simple example covers a 10° field at f/4.
Really short focal length lenses are required to get wide fields of view. They have a problem opposite that of long focal length lenses, so the solution is (obviously) to use a telephoto lens arrangement backwards. Although much more complex examples are common, this simple version covers ±40° at f/8.
The ultimate wide angle lens is one that no longer attempts to correct distortion, giving the picture the well-known appearance in which the nose of a person (or dog) looking at the camera looks way too long. These lenses can be made so that the image includes objects that are behind the photographer. In other words, the half field angle exceeds 90°. The example is a 10 element, f/3 fisheye lens that covers 180° full field.