In photography, there are three types of lenses: wide angle, normal and telephoto (zoom). Each lens is made up of many smaller simple lenses, which combine to give it its designation.
There are two categories of simple lenses: convex and concave. Within these two categories, there are three lenses: plano, positive/ negative meniscus and bi. This means that there are six total simple lenses, which are used in the construction of photography lenses.
Generally, convex lenses make the light converge and concave lenses make it diverge. This creates a focal point and image behind the concave lens and in front of the convex lens. The equation which describes the image of the object is given by
1/S(i)+1/S(o)=1/f
Where S(i) is the distance from the lens to the image, S(o) is the distance to the real object and f is the focal length of the lens. The focal length is the distance from the lens to the point where the light converges and the image is created.
However, the equation above assumes that light is passing through a medium which will not slow it down (air does) and that the lens is of negligible thickness. The equation which accurately describes lenses, also called the lens makers equation, is
1/f=(n-1)[1/R(1)-1/R(2)+d(n-1)/(nR(1)R(2))]
Where f is the focal length, n is the refractive index (how much the medium slows light down), R(1) is the inner radius of curvature, R(2) is the outer radius of curvature and d is the thickness of the lens.
The magnification of a single lens is given by the equation
M=-S(i)/S(o)
When many simple lenses are combined together, photographic or telescopic lenses are made. This process is extremely complex, which is why telescopes and camera equipment costs so much. For instance, a two element lens will have nine variable: four curvature radii, two thicknesses of lenses, one distance between lenses and two different types of glass. The amount of variables rises exponentially when more lenses are introduced, which is why this is mostly done on the computer now.
All lens makers need meet three basic requirements:
1. The lens has to have sufficient optical quality to pass basic tests. 2. The weight, volume and center of mass all have to be reasonable. 3. The lens has to work in certain temperatures, pressures, vibrations, light conditions and must have electromagnetic shielding.
Lenses are designed using what is called paraxial theory. This theory basically makes a few assumptions about the light and tells the lens maker where to place different elements to achieve a determined outcome (for instance, a 35mm lens with an aperture of 2.0). Since this makes assumptions, lens maker later will have to adjust everything so it is perfect and makes no assumptions. The lenses are made, placed, and then the lens is tested. This process is repeated again and again until the lens is as good as can be, however, all lenses have some sort of downfall. This can be read about in the next section.