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.

The human eye is somewhat like a camera, inasmuch as you don't want to drop yours and break it. But more relevantly, the human eye is like a camera in that it also has a focal length. But whereas cameras, while sometimes being quite expensive and complicated, are engineered devices made out of mostly static parts, the human eye is made out of countless tiny cells, controlled by delicate muscles, and is always in the process of adjusting itself to conditions around it. And the eye's output is constantly sorted out by the entire physical and metaphysical machinery of the visual processing system in the brain.

I described that entire metaphor briefly, because while the entire subject of human visual focal length is perhaps fascinating on its own, but it literally and metaphorically ties in with the idea of the focal length of human thinking. While your eyes can focus at variable lengths, your mind is usually focused about thirty feet in front of you, although this can vary widely. Along with a focal length in space, people also have a focal length in time. Most people focus on events in the past few minutes to past few hours, with things closer or further away from that somewhat blurring.

This is all pretty obvious.

The interesting thing about focal length is when it changes, and trying to understand or remember states when our mental (and sometimes physical) focal length was at a different length than it normally is. Intoxicated people, whether on alcohol or something more exotic, have a very altered focal length, usually foreshortened, but sometimes lengthened. Children have a focal length that is much closer to what is in front of them, both in time and space. It is often hard to remember just how odd and distant the world outside our familiar homes were as children.

And, when you are depressed, say so depressed that you've been trying to write a basic write-up all day long and all your sentences come out jumbled and clumsy, well, your focal length is about six inches in front of your eyes, and even that is really too much.

The idea behind focal length as it relates to thought processes is fairly obvious, but some of the things that can be done with the concept are quite important, as I will be describing in my writings once I return to thinking, at least on a theoretical level, that life is not a long walk into despair.

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