Aperture and F-Stops

Ever wonder why there is such a discrepancy in price between a 50mm f/2.8 lens and a 50mm f/1.4 lens? (The price of the former is typically at least a third of that of the latter.) The answer simply is that 1.4 is less than 2.8!
Well, you may have heard the lens with the lower f/ (f-stop) value called the faster lens. The reason behind this is that in the same lighting conditions, a lens at f/1.4 will be able to shoot an exposure that is shorter than what the f/2.8 is capable of. In other words, the shutter speed is faster. A bit of common sense and deduction can tell you that the faster lens must be able to let more light in than the slower one in the same amount of time. That's where the f-stop comes in. For the mathematically minded, f-stop = f/d, where f is the focal length of the lens and d is the diameter of the aperture. In the case of lens specifications, the f-stop (e.g. f/1.4) that is listed next to the focal length of the lens (e.g. 50mm) refers to f/D, where D is the largest diameter that the aperture can reach. Translated into practical knowledge, when you cut the diameter in half (or double the f-stop), you quarter the amount of light that gets through since it is the area of the opening that controls how much light passes.
So, there are a couple of things to consider with these so-called faster lenses. First of all, faster lenses are typically larger and heavier. Faster lenses need to be wider since they have to accommodate for the bigger diameter. They are heavier because they contain more or bigger glass elements. Secondly, because more glass elements result in more optical distortion, specially coated glass and aspherical elements have to be used. These factors add to the price of the lens.
But, if you can put up with the extra bulk in the camera case and the reduced bulk of the wallet, a faster lens can open up some creative portals. If anything, it will allow you to take more shots without having to pull that tripod out. The creative aspects are related to your use of depth of field.