Have you ever wondered why wide angle lenses such as Sigma 10-20mm f/4-5.6 EX DC HSM
Well, this is a reasonable question if your understanding of optics is not much beyond the simple thin lens model you learned in high school. Photographic lenses are not thin lenses. Even the simplest prime lenses are constructed with multiple lenses in multiple groups. These are called “thick lenses”. The effective focal length of the thick lenses are no longer the distance between the last optical element to the rear focal point (called back focal length). To make the wide angle length work on SLR cameras, the back focal length of the lens needs to be longer than the effective focal length so the mirror doesn’t hit the lens when the shutter is release. On the opposite, for telephoto lenses the back focal length needs to be shorter than the effective focal length. This is typically achieved by putting a concave lens (or negative lens group) or convex (or positive lens group) at the front for wide angle and telephoto lenses, respectively.
The modern day wide angle lenses were mostly inspired by the old but clever design called retrofocus lens design pioneered by a French engineer (a little more history can be found here). If you compare the original retrofocus lens and the aforementioned Sigma wide angle lens, you can notice the similarity. The Sigma lens used a group of concave lenses instead of single concave lens for the front element in the original design.
If you are interested in digging into lens design, there are many good books, for example, Applied Photographic Optics by Sidney Ray. However you can learn quite a lot without spending a dime from free online resources by using search engines.
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