Focal length, or focal length range in the case of zooms, will usually be the foremost consideration when choosing a lens for a specific photograph or type of photography. The focal length of a lens determines two characteristics that are very important to photographers: magnification and angle of view.
Longer focal lengths correspond to higher magnification and vice-versa. Wide-angle lenses with short focal lengths have low magnification, which means you have to get physically close to an average-size subject to fill the frame. But that also means you can fit large subjects in the frame without having to shoot from a distance. Telephoto lenses with long focal lengths have high magnification, so you can fill the frame with subjects that are further away from the camera.
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The focal length of a lens is defined as the distance from its secondary principal point to its rear focal point when focus is set to infinity. The secondary principal point is one of six "cardinal points" that are used as points of reference in an optical lens (front and rear focal points, primary and secondary nodal points, and primary and secondary principal points). There's no predefined location for the secondary principal point in a compound lens—it could be somewhere inside the lens barrel or at some point outside the barrel, depending on the design of the lens—so there's no easy way to accurately measure the focal length of a lens yourself.
"Angle of view" describes how much of the scene in front of the camera will be captured by the camera's sensor. In slightly more technical terms, it is the angular extent of the scene captured on the sensor, measured diagonally. It is important to remember that angle of view is entirely determined by both the focal length of the lens and the format of the camera's sensor, so the angle of view you get from any given lens will be different on 35 mm full-frame and APS-C format cameras. Different lenses of equal focal length will always have the same angle of view when used with the same-sized sensor.
With long focal lengths, foreground and background objects will often appear to be closer together in the final image. This effect is sometimes called "telephoto compression", although it is not actually caused by the lens itself. What really happens is that when using a telephoto lens, you will need to be further away from your subjects. So, relative to the distance from the camera to the foreground and background subjects, they actually are closer together. Another way of saying this is that since both the foreground and background objects are at a considerable distance from the camera, their relative sizes in the final image will be closer to reality. When shooting with a wide-angle lens you normally need to get close to the foreground subject so that it is sufficiently large in the frame, which is why more distant objects look comparatively smaller. The difference in apparent perspective is actually a result of how far you are from your subject.