Focal Length

The focal length of a camera lens describes the effective distance of the pinhole from the film that the lens acts like.

To put it in plain English, a lens of focal length of 50 mm (the "normal" lens for 35 mm film) will project the same size of image on the film as a pinhole located 50 mm in front of the film.

The "normal" focal length is such that the resultant image looks essentially the same as if viewed by the human eye, and is typically the size of the diagonal of the image on the film.

For example, 50 mm is "normal" for 35 mm film, 150 mm is "normal" for 4"x5" film, 300 mm is "normal" for 8"x10", etc.

A focal length higher than "normal" produces the telephoto effect; one lesser than "normal" produces wide angle images.

Suppose you build a 4x5 view camera and instead of buying an expensive lens just drill a pinhole, you can change the "focal length" by simply moving the front of the camera away from or closer to the film. You will have a perfect zoom capability. Move the pinhole 150 mm (6.8") in front of the film for a "normal" image. Move it forward (away from the film, and you can take telephoto pictures. Move it back (toward the film), and you can take wide angle shots (though these may not fully cover the film edges - the "normal" and telephoto ones, however, will).

Just remember that if you do that, your f-stop changes, hence you need to adjust the exposure time accordingly.

A longer focal length lens will project a magnified view of a smaller area of the scene, whereas a short lens will project a view of a larger area of the scene (wide angle).

With a bit of maths, it's possible to determine how much of the scene you will capture, and draw a diagram to help yourself out.

I will compare a 28mm (wide angle), 50mm (normal) and 135mm (telephoto) lens for 35mm film.

Taking a table of viewing angle according to focal length,

FL    Long Side  Short Side
28mm     65°         45°
50mm     40°         27°
135mm    15°         10°

we can determine the effective amount of the image from the rule:

w = d×tan(0.5×theta)

Where w is the width of the image (or height on the vertical side), d is the distance from camera to object and theta is the angle taken from the previous table. (We can ignore all constants, since we're only interested in ratios).

This gives (for d=100):

FL    Width Height
28mm   65     46
50mm   40     27
135mm  15     10

Now draw concentric rectangles of these dimensions (probably using mm as a scale), and the comparison should become obvious if you imagine a scene drawn within. Ideally, you should hold the diagram at a distance d from your eye (100mm in this case).

       +-------------------------------+
       |                               |
       |                               |
       |      +-----------------+      |
       |      |                 |      |
       |      |     +-----+     |      |
_______|______|_____|__135|_____|______|__(Scene horizon)
       |      |     +-----+     |      |
       |      |               50|      |
       |      +-----------------+      |
       |                               |
       |                             28|
       +-------------------------------+

Obviously, this is only a rough guide, but may be useful if you're trying to select a lens to complement your others.

Also worthy of note, is that the focal length of a lens is infinitessimally larger than the theoretical minimum distance that an object can be placed to the lens and still focused sharply. At the focal length, the image rays will be parallel. Just inside the focal length, the image rays will converge at a huge distance. Therefore, for practical reasons, the minimum distance of focus is usually significantly larger than the focal length of the lens.