Up to this point we have been using simple lenses to discuss optical concepts. A simple lens is just a single lens that can be used to approximate a much more complex real-life lens. Photographic lenses are anything but simple. They generally contain multiple elements (typically 4 or more), positive and negative, that combine to form a lens of a specific focal length.
Multiple lens elements are used in photographic lenses because you need those extra elements to correct for aberrations. Aberrations are inconsistencies in the way that light is focused and present in all lenses to some degree. First, light comes in different wavelengths (different colors) and each of those colors is bent slightly differently. This leads to color fringing or chromatic aberration. Second, lenses have spherical surfaces because spherical surfaces are easy to produce. The problem is that spherical surfaces are not ideal. Spherical surfaces lead to a whole host of other aberrations that will degrade the image quality. These aberrations are a big problem with a simple lens, but they can be mostly eradicated with multiple well-chosen elements, fancy glass (such as ED glass) and the occasional aspherical lens element. Designing a lens is extremely complex, but the end product is a lens that produces a sharp image from corner to corner with good color correction and limited distortion.
A few examples of lens aberrations: The first example is that of distortion. Distortion is caused by unequal magnification across the field. The field may be entirely sharp with this aberration - it's not a fuzzy aberration. In this case it is called barrel distortion. This picture was shot with my old Nikon 5400 at maximum magnification. You can see the center of the image appears bloated. There is an opposite situation called pincushion distortion where the center of the image appears sucked in.
The next example is a chromatic aberration. The picture is just a close-up of the lower right corner of the above image. You can see blue and red color fringing around the black bars. The colors are not focusing at quite the same place on the image. You can also see that the left part of the image (closer to the center) is less affected. This aberration tends to worsen as you move from the center to the periphery.
The last example is kinda a mishmash of aberrations that worsen in the periphery of the image including: spherical, coma, astigmatism, field flatness. The center of the image is sharp and periphery is markedly not so. It's hard to separate these aberrations, so I won't try. They all lead to fuzziness on the periphery and good lenses will tend to minimize them.
Focal length can also be measured in diopters (1000/focal length in mm). A 100mm lens can also be described as a +10 diopter lens. Shorter focal length lenses will have a higher diopter value and will bend light more than a longer focal length lens.
The focal length can be measured from either side of the lens - the lens has a front focal length and a back focal length. A 25mm lens is a 25mm lens whether I look at it from the front or the back. I can flip the magnifying glass over and still burn the same ant at the same distance.
The end result is that the focal length represents the distance that an object at infinity will be focused behind the lens. The focal length is a very important number and determines many aspects of macro photography such as extension, magnification, working distance and will regularly show up in the coming installments.