If I have a +1, +2, +4, or +10 close-up lens which attaches to the front of my regular lens, how can I calculate its effect on close focusing distance, figure out how much magnification I can get from the combination, and tell what size of object will fill the frame at the closest distance?
It is really rather simple. The diopter value will tell you how close you must be to the subject of your photograph, the farthest distance you can get a sharp image with the close-up lens on. you divide one metre by the diopter value to get the distance, which is the focal distance of the close-up lens.
Hence a +1 lens will give a far distance of 1 m and the +2 lens will give a far distance of ½ m the +4 lens will provide a far distance of 25 cm (¼ m) and finally the +10 lens will have a far distance of 10 cm
All those distances are measured from the attached lens.
The closest distance is a trickier subject. It depends on how close your original lens will focus and how far it extends from the sensor. If you measure the distance from its front end at its closest focusing distance and divide one metre by this distance, you get a diopter value that corresponds to the focusing range of the lens.
If you have one of the more common kit zoom lenses, it might be 18-55 mm and focus down to about 30 cm from the sensor. The front end of the lens is about 20 cm from the subject when it is at its closest, which corresponds to about five diopters or perhaps somewhat less. Hence adding one or two diopters won't make much difference on its closest distance, mostly it will just degrade image quality.
Only the ten diopters lens will provide a substantial advantage regarding image size and close distance, but at the price of severely degraded performance, as simple lenses like this are rife with lens aberrations, as colour aberration, coma and distortion. The result is that you cannot take a sharp picture at all with the ten diopters lens attached.
Looking at it from a brighter side, you might have a tele lens or a tele zoom lens, which focuses only down to about one metre. Adding a one diopter lens will take you to distances between one metre and a half metre and two diopters will give you even closer range, without sacrificing so much image quality as with the ten diopters lens. The one diopter and two diopters lenses can be very useful with a tele zoom. The one diopter will double the reproduction scale if your lens otherwise focuses only to one metre. And the two diopters lens will more than triple it.
It should be remembered that you can never focus to a larger distance than the focal length of the attached close-up lens, so with one diopter it is one metre from the lens and with two diopters it is 50 cm from the lens. Farther distances are not possible.
For higher diopter values than 2 you would need an achromatic close-up lens to get sharp images. Those are more expensive than simple lenses, but perform much better. With a tele zoom and an achromatic close-up lens, you may achieve performance much like a real macro lens when you take pictures of natural objects, where straight lines and curvature of field are not important. However, it is not suitable for reproduction of flat or rectilinear objects, as it will still give distortion and curvature of field, and it will have some coma error as well. The only correction of an achromatic close-up lens is colour correction, which makes images sharper with less fringing toward the edges of the image.