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Every lens has different focal length in terms of millimeter so if I have a 100mm lens, what does that refer to? Does it mean the length of the lens itself is going to be 4 inches long, or does this refer to something else?
What does it actually boil down to when I zoom in to 250mm? How does the "size' of the lens translate to how much you can zoom? What is it about the construction of the lens that makes it be X mm?
The number of millimeters is the focal-length. This is not the size of the lens but it is loosely related. If lenses where made of a single glass element, it would be the much closer to the lens length plus flange distance of the mount. Modern lenses are made of considerably more elements so there is no simple relation.
The most important thing about focal-length is that, when combined with sensor-size, it defines the angle-of-view. Lenses which have shorter focal-lengths have a wider angle of view. Lenses with longer focal-lengths have a narrow angle-of-view. This is why a longer focal-length is seen as more zoomed in on a given camera.
Zoom lenses are defined by a range of millimeters, say 50-200mm, which means the focal-length can be adjusted anywhere from 50 to 200mm.
The value in millimetres is the focal length. A lens with focal length of 100mm will bring parallel rays of light (from an object very far from the camera) into focus 100mm behind the lens.
So clearly if the mountains come into focus 100mm behind the lens, then the length of the lens barrel must be 100mm minus the distance from the sensor to where the lens mounts. Closer objects will be brought into focus at greater distances, so to be able to focus closer the lens has to be able to extend to move further from the camera so the barrel would have to be longer.
Now that is for a single thin lens. A multi lens system a with focal length 100mm will bring the mountains into focus 100mm behind the rear principal plane. This is an imaginary plane the location of which depends on the properties of the lens elements. Telephoto designs move the principal planes forward meaning the physical length of the lens barrel can be less than the focal length.
Focal length also determines angle of view, but it is co-dependant on the size of the film or sensor. This is why it is important to understand the definition of focal length given above, as people tend to say mounting a 100mm lens on an APS-C camera body makes the lens 150mm, this is not true, a focussed image is still formed the same distance from the principal plane, it merely makes the field of view the same as a 150mm on a 35mm sensor.
What it actually measures is the angle of view.
The focal length is the distance from the center of a theoretical single lens element to the photographic media (camera sensor) that would give the same angle of view as the camera lens.
A camera lens contains a lot of lens elements, so the size of the lens can be considerably shorter or longer than the focal length. Generaly a longer focal length means a longer lens, but not always. For example, I have a zoom lens that actually expands when the focal length gets shorter.
