In photography, the focal length of an optical system measures how strongly it converges light onto the photographic medium (either film plane of the sensor of your digital camera).
It can be thought of as the distance between the optical centre of a lens, to the film/sensor.
A longer focal length, or lower optical power, is associated with larger magnification. That's why you'll see those sports photographers out on the sidelines of the field with those massive cannons of lenses; Because of the huge magification those long barrels/long "focal lengths" provide.
A shorter focal length, higher optical power, is associated with a lesser magnification, but greater angle of view. Anything less than 50mm focal length (on a 35mm camera or equivalent) is considered a "wide angle" lens; Meaning a large amount of the peripherals of a scene can be recorded by the camera. This is why wide-angle lenses are popular with photojournalists, news photographers and architectural photographers.
A comparison of a long focal length (narrow angle of view) to a short focal length (wide angle of view) from the top of my street in Maraval, Trinidad.
Short focal length. Notice the wide field of view.
From the same position, but with a long focal length. The magnification is greater, but less is visible in the shot, neither does the street doesn't look as yawning. This is because the perspective lines aren't as warped as with the short focal-length version. This is also a long exposure photograph, which is why the family walking up the street are motion blurred.
Wide-angle lenses, however, are also associated with a warping of perspective lines (by the very nature of having a high optical power) so they are a bad choice for most product or portrait photography, unless you're after a more warped effect. In Sitepoint's Photography for the Web book, Paul Duncanson has a great example of what would happen if you photographed a headshot wide-angle; Big nose, small ears, warped forehead. It's not pretty.
So. I took my new Canon PowerShot SX120 (compact cam) out for a spin this week. While waiting on a friend, I wandered around a park in Port of Spain, photographing statues and passing traffic using narrow and wide angles (short focal length and long focal length). Here they are below. I hope you can see the effect.
A STATUE OR BUST
In Memoral Part, Port of Spain. Made to honour those who died in WWII (Trini history is mixed up in there too, believe it or not).
Note the use of a short focal length/wide angle of view to exaggerate the perspective. For this type of shot, I should have positioned myself more directly into the middle of the path, so as to get better symmetry.
A BUS OR TAXI
A wide angle used, and low to the ground, to make the street look broader and to get the waiting passenger into the frame.
A "maxi-taxi". These mini-buses are about as Trini as it gets. Travelling in one isn't for the faint of heart.
Long focal length used to keep the lines of the box straight and clean.
FAST FOOD RESTAURANT
An arabic food eatery nearby where I live. It's a tiny, little place, but decent food and nice people. I ordered a gyro, then sat down snapping away with my Powershot, using a short focal length to make the room seem bigger, and to get as many details of the store in as I could. The counter, the menu, the Coca-cola machine, and the food in front of me hopefully come together to express that this place is an eatery.
On a 35mm film camera, 50mm is considered a "normal" lens. Meaning that it is roughly similar to what human eyes see. Anything over that is "telephoto", anything under is "wide". These numbers are different for different dimension cameras, but usually manufacturers will print the focal length equivalent in terms of 35mm film cameras in the specs.
For my Powershot, for example, the actual focal length of the lens is 6mm - 60mm. In their specs, however, they list the equivalent focal length as 36mm - 360mm; Meaning if you scaled up the compact cam to 35mm film camera dimensions, that's what the focal length will translate to.
Anyways, I hope this made sense this week. I hope the numbers and terms weren't too confusing. Just remember;
Short length > Wide angle
Long length > Narrow angle
If my week allows, I'll be back next weekend with some examples of long-exposure photography.