If you don't have a lens that focuses sufficiently close, you can mount a diopter lens in front of one of your camera lenses. The magnification that you can attain depends on the strength of the diopter (i.e., its focal length) and the focal length of your camera lens. I will not discuss here how to compute the maximum magnification of a specific combination of diopter and camera lens, because this involves several factors besides the two focal lengths. As a rule-of-thumb, given a diopter lens of a certain strength, a camera lens with a long focal length will be more strongly affected by it (i.e., it will focus much closer than without the diopter) than a camera lens of short focal length. Another important rule is that the shorter the focal length of a lens, the shorter is its working distance at a given magnification. This applies also to the combined focal length of a lens + diopter.
Diopters are lenses consisting of a single element, or sometimes two elements glued together to correct chromatic aberrations. Diopters are usually mounted in a metal ring similar to that used for filters that screw onto the front of camera lenses, and are attached to a lens in the same way as filters. Diopters, as used in close-up photography, are convergent lenses, i.e., they focus parallel incoming rays of light to a point on the opposite side of the lens, usually some distance from the lens itself.
Cheap diopter lenses are plano-convex or covexo-concave lenses, not unlike those of eyeglasses. They give only mediocre to moderately good results. More expensive diopters are achromatic doublets (i.e., two lenses of different materials cemented together). These lenses, also called achromats, give far better results. Good diopters are also coated with anti-reflection layers on both surfaces. Nikon markets two such lenses, models 5T and 6T. These are often difficult to find, and the Canon 500D is a good alternative. A further advantage is that the Canon diopter is manufactured in several sizes.
The choice of a camera lens to combine with a diopter depends primarily on which lenses you have available. You should choose a lens of good quality, because adding a diopter may magnify the faults of the lens. You should also not use a lens of short focal length, because achieving a sufficient magnification will involve using a strong diopter (strong diopters tend to have correspondingly strong optical aberrations) and will give you a very short working distance. Camera lenses with an excessively long focal length should also be avoided, because they tend to have a long minimum focusing distance to start with, and a small range of focusing distances when a diopter is added.
The best camera lenses for this purpose are those of fixed focal length (as opposed to zooms, although the latter can also be used). A lens with a focal length of 50 to 135 mm is most practical for this use. The strength of an appropriate diopter depends on the magnification to be attained, and on the focal length of the lens being used. Stronger diopters must be used for higher magnifications and lenses of shorter focal lengths.
Diopters can be used also with cameras that don't have interchangeable lenses. In fact, for these cameras they are the only method available for reducing the minimum focusing distance. Most modern point-and-shoot digital cameras can focus to a very close range, and can provide surprisingly good performance in close-up photography. Their main drawback is that the working distance typically is extremely short (frequently, 10 to 40 mm at maximum magnification). This makes it difficult or impossible to place light sources in appropriate positions around the subject (especially, close to the optical axis of the lens). In this situation, diopters cannot help.
A lens is a lens is a lens
There is some confusion in the use of the term lens. Basically, a lens is a sheet of transparent material that changes the direction of light rays passing through it. Typically, one or both surfaces of a lens are curved, but this is not an absolute requirement. There are holographic lenses, for instance, that have flat sides and bend light by passing it through a microscopic, laser-etched pattern embedded in the lens material. Out in the universe, there are gravitational lenses that bend light just by attracting the mass of photons. The lenses used in eyeglasses and cheap magnifiers normally are made of a single optical element (i.e., a single piece of a homogeneous glass or plastic). These can be called simple lenses. The lenses used in cameras, instead, usually are made of a stack of several optical elements. Each of these optical elements is also a lens. Optical elements may be glued together, and therefore a group of these lenses may appear to an observer to be a simple lens (but its optical properties are of course different from those of a simple lens).
Camera lenses are of course very different from a simple, unmounted lens. Camera lenses are made up of a complex set of optical lenses, precision mechanics and electronics, and may contain over a hundred separate parts. It is unfortunate that, in the English language, the term lens is used also for camera lenses. Other languages use distinct words for simple lenses and camera lenses.
To add to the confusion, one sometimes encounters the term lense. It may be used to indicate a camera lens. In spite of what some people may tell you, a lense is exactly the same thing as a lens. The lense spelling is just old-fashioned, like in the expression ye olde shoppe.
Diopters (also called diopter lenses or add-on lenses) are also lenses. In this web site, normally I use the term lens when speaking of camera lenses. In the case of diopter lenses, I just call them diopters to make it clear when I am talking about the camera lens, and when I refer to the diopter lens.
How many diopters in a diopter?
A further source of confusion is that a diopter, or dioptre, is also a measurement unit that expresses the power of a lens. I am not using these units in my web site, but you may encounter them elsewhere. In practice, for a converging lens the strength in diopters (D) is given by D = 1000 / f, where f is the focal length in mm. therefore, a lens with a focal length of 200 mm has a strength of 5 diopters. Therefore, you may choose to express the strength of a lens either in focal length or in diopters - it is just the same thing expressed with two different measurement units. In this web site, I always use the focal length because this is the measurement normally used for camera lenses. The strength of eyeglass lenses, instead, is normally given in diopters.
Cheap diopter lenses for close-up work often come in sets of three, with strengths of 1, 2 and 3 diopters. Achromatic diopter lenses may have higher strengths (roughly between 5 and 10 diopters). An even higher diopter value requires a lens design consisting of several optical elements, in order to better correct the inevitable optical aberrations.
The strength in diopters can be specified also for diverging lenses, but in this case the value in diopters is negative. This expresses the fact that the focal point of a diverging lens is located on its opposite side, with respect to a converging lens.
When to use diopters
Diopters are likely to work acceptably when used at close-up distances, but reaching the macro range (i.e., 1:1 or higher) with diopters and achieving good quality is difficult. At 1:1, the focal length of a diopter must be equal to that of the lens, and the optical aberrations introduced by diopters of short focal lengths are conspicuous. In fact, at this magnification it is easier to achieve good results by attaching a reversed camera lens in front of one mounted normally. The added lens will work like a diopter, and likely will provide a better correction of aberrations than simple or achromatic diopters. Problems connected with reversed lenses are discussed here.
Some photographers have reported better results with a lens and moderately strong diopters of good quality, than with the same lens mounted on extension rings. The reason for this is likely that the lens used is a general-purpose type not optimized for close-up work. Increasing its distance from the focal plane by using extension rings forces it to work outside the focusing range for which it is optimized, while using a diopter does not do so (although it does introduce aberrations produced by the diopter). This is less likely to happen with lenses designed for macro and close-up photography (albeit, in this case most macro lenses should be able to focus at the desired distance without using extension rings). Special diopters matched to a particular model of macro lens, and apparently providing very good results, occasionally have been manufactured. If I remember correctly, such a diopter was available for the Olympus 80 mm macro lens.
It is also possible to use diopters and extension rings at the same time, although only experimenting can tell you if this provides any practical advantage over using either one alone.
Diopters may be the only way to perform close-up photography with wide-angle lenses. Because of the short focal length of these lenses, it may not be possible to use extension rings. For instance, a 10 mm super-wide-angle requires an extension ring of about 3 mm to achieve a reproduction ratio of about 1:3. Unfortunately, the shortest extension rings are about 9 to 11 mm thick, which implies a reproduction ratio of about 1:1. At this reproduction ratio, the subject would have to be placed inside the lens to achieve focus. There may be practical problems in using diopters with super-wide-angle lenses. For instance, for a diopter to be useful, the focal length of the diopter must be of the same order of magnitude (usually, 2-5 times longer) than the focal length of the lens. The diopter must also be large enough to mount in front of the lens without causing vignetting. A large diopter of short focal length (assuming one can find such an add-on lens) may introduce strong aberrations, thus making it useless, except as a novelty for special effects.