INTRODUCTION

I remember one sunny afternoon -about forty five years ago- in downtown Mexico City, glued to the window of Foto Rudiger, looking in awe at hundreds of lenses in display. Why are there so many lenses? I asked my father. His answer: "Because lenses are designed for specific purposes, subjects, situations and needs, including budgets."

That afternoon -around several cups of Brazilian coffee- I also learned that all laws have as reason to exist the promotion of a good and/or the avoidance of an evil, and that physics laws of optics are not different. And so, lenses designers look at ways to apply those laws better and better, to promote greater magnification with amazing detail or wider splendid vistas, avoiding distortions and other aberrations as much as glass technology allows at the time. 

I also learned that afternoon that the selection process needs not to be a puzzle; once your own set of variables is clear in your mind, choices pop up at you by themselves. That simple. To tackle this subject comprehensibly, although seemingly an enormous task, it is not.

The reasons for the initial overwhelming are, mainly: the wide variety of both lenses offerings and the variety of needs of each individual photographer (the set of variables): 

USE	The primary interest (sports, fashion, portraits, landscapes, wildlife, architecture, weddings, photojournalism, macro, travel, etc.)
BUDGET	Which comes immediately into mind, especially if one selects more than one interest; and the seriousness of the photographer, really meaning how much can that budget be stretched.
BODY	What camera is in use; what others are being considered.
LENSES	What other lenses may already be in the bag.
MEDIA	Film or digital; is there a transition from one media into the other in the near future, and so on

Let's look first at the basic characteristics of lenses to later match them to our own set of variables.

Lenses can be classified according to focal length, its variability, focusing method, and its relative speed as follows:

FOCAL LENGTH: Fish-eye; wide angle; normal; short, medium and long telephoto
Focal length 35mm Angle of View* Typical use Example  Fisheye 6 - 16mm 220° - 180° Enclosed spaces 8mm f/2.8  Wideangle 17 - 35mm 114° - 62° Landscape 24mm f/2.8  Normal 45 - 55mm 51° - 53° General 50mm f/1.8  Short telephoto 85 - 135mm 28° - 18° Portraits 85mm f/1.4  Medium telephoto 180 - 300mm 13° - 8° Sports 300mm f/2.8  Long telephoto 400 - 1000mm 6° - 2.5° Wildlife 500mm f/4 Zoom lenses have now crossed the typical categories above, in an effort to widen the range of applications a single lens can be used for.
VARIABILITY OF FOCAL LENGTH
•	With fixed focal length or "prime" lenses
•	With variable focal length or "zoom" lenses
	• Zoom lenses with variable "speed" or aperture • Zoom lenses with constant maximum "speed" or aperture
FOCUSING METHOD
•	Manual focusing or "MF" lenses (Rotating a ring in the lens barrel)
•	Auto focusing or "AF" lenses (Depressing the shutter button on an automatic camera)
"SPEED" or "LUMINOSITY" in terms of how much light they allow into the film or digital sensor at its widest aperture
•	With a small f/stop number, wide aperture, "fast" (f/1.4, f/2.8)
•	With a not so small f/stop number, not so wide aperture, "slow" (f/4, f/5.6)

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* FOCAL LENGTH AND ANGLE OF VIEW Focal length is the distance between the lens node of emission to the plane at which objects at infinity are brought into focus to form a sharp image; i.e. at the film or sensor plane in a camera. The focal length determines the size of the subject image on film when the lens is focused at infinity.

The angle of view (AOV, sometimes referred to also as Field of View) is the angle covered by a lens of given focal length at infinity. Typically it is measured diagonally and for a given film or digital sensor format. In a rectilinear lens, it is possible to approximate it with the formula AOV = 2 arctangent [x / (2 f)], where "x" is the diagonal of the film (43.2666mm for 35mm format) and "f" the focal length in mm¹.

In practice, with complex optical formulas employed in modern lenses, the AOV has to be measured with specialized instrumentation. But the important thing is that the angle of view is inversely proportional to the focal length, so the shorter this is, the wider the AOV and viceversa. Also, to increase the focal length to twice, reduces the AOV in half.