If I look up the specifications of my 50 mm lens, it says that it has 8 lens elements, in 7 groups. Why is this, why not just a single lens element with a 50 mm focal distance?
Single lenses with real thickness refract the different wavelengths of light at slightly different angles. For anywhere other than the exact optical center of the lens, this causes a prismatic effect that gets more noticeable as one moves further from the optical center of the lens. This is what we refer to as chromatic aberration. It isn't the only optical aberration we encounter when using a single lens element, but it is probably the most noticeable one.
The earliest spyglasses (telescopes) suffered greatly from CA and the other optical aberrations. The field of optics developed to deal with these imperfections as they applied to telescopes well before the beginning of photography in the mid-19th century as a means of preserving a scene projected by a lens using light sensitive chemicals.
In the 1600's, Snellius (the origin of 'Snell's Law') and Descartes (the creator or Cartesian geometry) codified the earliest laws of refraction and reflection. By 1690 Christiaan Huygens had written his 'Traité de la Lumière' or 'Treatise on Light' that built on Descartes' work and presented the wave theory of light, first presented to the Paris Academy of Sciences in 1678, based on mathematics. Isaac Newton published 'Hypothesis of Light' in 1675 and 'Optiks' in 1705 in which he presented a competing theory of light as corpuscles, or particles. For the next hundred years or so, Newton's theory of light was accepted and Huygens' wave theory was rejected. It was not until Augustin-Jean Fresnel adopted Huygens' principle in 1821 and showed that it could explain the rectilinear propagation and diffraction effects of light that Huygens' wave theory was generally accepted. This principle is now known as the Huygens–Fresnel principle.
Newton also demonstrated that a prism decomposes white light into a spectrum of its component colors, and that a lens and second prism can be used to recompose the multicolored spectrum back into white light that had the same properties as the light before it struck the first prism. Although the particulars of Newton's corpuscular theory has been shown to be mostly incorrect, his breakthroughs with regard to color and refraction, along with similar work by Huygens, are what led to the development of compound lenses to correct for chromatic aberration.
Huygens built his own compound telescopes, without the benefit of yet to be developed achromatic lenses, that required long distances between the front and rear elements. Newton did not do any further refractive lens development himself. He preferred to work around the problem altogether by using curved first surface reflective mirrors to avoid the aberrations caused by refraction. In fact, he famously declared that chromatic aberration could not be corrected because he failed to consider one could use two types of glass with different refractive properties.
The first achromatic lens was created in 1733. It used two elements with different refractive indexes to partially correct for color aberrations and allowed refractive telescopes to be made shorter and more functional.
The three element apochromat soon followed, which was an even better improvement over the two element achromat than the achromat had been over the simple lens.
Much of what lensmakers learned correcting for chromatic aberration also had application to the other, monochromatic, optical aberrations inherent in a simple lens.
Once chemical photography emerged in the 19th century as a way to preserve an image projected by a lens, those who made lenses for photographic use took what had been learned earlier in the field of optics, which had mostly been applied to telescopes and the like, and ran with it. A good survey of the developments in photographic lens design, all based on the optical principles discovered in the 17th and 18th centuries discussed above, can be found in the 'History of Photographic Lens Design' article at Wikipedia. (It's far too long and involved to include a summary here.)
In all there are seven "classic" optical aberrations that compound lenses attempt to correct to varying degrees. Note that these aberrations are not the result of imperfections in the construction of lenses, but are due to the nature of light itself as it passes through refractive materials. These aberrations would be present even if those refractive materials were mathematically perfect.
- Defocus (the lowest order which is easily corrected by changing the distance between the lens and the imaging plane)
- Spherical Aberration
- Field curvature
- Geometric distortion
- Chromatic aberration
You can do this. Your images, quite simply, won't be very good, though.
It was learned early in optics - way back in the Galileo Galilei days of refractor telescopes and monoculars - that a single glass element doesn't create a very good image. It tends not to be sharp; it tends to have colour fringing (because the colours don't focus at the same point); and it tends to have distortion.
Done right, adding additional elements can neutralize most to nearly all of these bad behaviours. Images sharpen; distortion goes away; colours focus together. Adding more elements does have its own issues, though. Each air-to-glass surface reflects a little light away. Modern lenses have multicoating layers to minimize this, but if you have enough elements, the loss of light starts to be noticeable and can negatively affect your image by causing flare.
So, as a result, normal lenses (50-ish mm lenses for full-frame cameras specifically) tend to have between four and eight elements (pieces of glass). Five to six works really well in most cases, but digital cameras are more sensitive to colour fringing than film is, so high-end normal lenses can have more elements than this to maximize correction. Modern multicoating makes this not as much of a problem as it was even twenty or thirty years ago.
Zoom lenses handle a range of focal lengths, so need even more correction, so you'll see ten, fifteen, even twenty or more elements in such lenses at times.
Let me give one short (and not full) answer about the reasons behind many elements. In every element you have kind of barrel/pincushion aberration and additional elements "fight" in some degree with this.
Also (as far as i know) is better to put aperture mechanics between elements (the need to achieve even illumination over the whole sensor/film plane).
Autofocus mechanic will need to be quite powerful (f/2 will mean 25 mm diameter of element) because of need to move relatively heave glass element.
And if you have image stabilization this is one group (of one or more elements). If you have only one element the construction will become quite complex and you can't reach this level of stabilization. Also you will be very limited in sense of open apertures because you will need to move one huge element.
Some simple cameras can get by using a single-element lens however the image realized is second-rate. Nowadays, even relativity inexpensive cameras are fitted with as many as seven individual lens elements. If the camera lens is of the single element type, the image will be marred by several defects that fall under the heading “aberration”.
One such aberration reveals color flinging whereby a multi-colored, rainbow effect is seen surrounding the objects being images. What is happening is; each of the various colors that comprise the vista are brought to a focus at slightly different distances from the lens. Violet light images, being the most refrangible, comes to a focus first, red images being the lease refrangible, come to a focus further downstream. The images consisting of other colors fall somewhere in-between. This phenomenon is called chromatic aberration.
Now the further away from the lens an image forms, the bigger it will be. In others words, a lens suffering from chromatic aberration projects multiple images, each will differ in size. The result is the color flinging most associated with chromatic aberration. Actually there are two types, longitudinal and transverse. We can reduce the harmful properties of chromatic aberration by the use of a doublet (2 element lens). One is made using crown glass and the other flit. One has strong positive power the other weak negative power. When sandwiched together, the combination midrates chromatic aberration. This 2 element design corrects just two colors, we can add a third lens making the sandwich an achromatic triplet (achromatic Greek for free of color error).
In addition to the plague of chromatic aberration, there are 6 other major aberrations (mentioned by others on this post) that can be mitigated. Technically, each requires a specialized lens as to shape and material. All this and more, forces the lens designer to construct a multiple element lens. Some of the elements are cemented together; some are air-spaces, some move as a group as you zoom and focus.
Bottom line: The faithful lens has yet to be made. Hats off the opticians who create these marvels for our use and enjoyment!