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If you are changing from f/2 to f/2. 8, you are halving the exposure. In doing so, you're halving the open area of the aperture in the lens. By this, you are allowing 50% less light through the lens (1 f-stop). This is because the f-stop numbers come from an equation used to work out the size of the aperture from the focal length of the lens. Let's say you are photographing portraits of someone at the beach during sunset. As the sun keeps going down, you will have less and less light which you need to compensate somehow. One of the possible solutions is to open up your aperture, letting in more light through the lens onto your camera's sensor. Jumping up an f-stop will brighten up your image but also cause a change in the depth of field. If you are shooting with a wider aperture such as f/2. 8 you will notice that the area of focus is much smaller than if you were using a bigger f-stop, for example, f/5. 6 or f/8. So to put it this way: The wider the aperture is, the shallower the depth of field.
Note: The "A" setting on your shutter-mode dial does not always mean "Automatic. " Unless your digicam has separate settings for both modes, the "A" frequently stands for "Aperture Priority, " a mode in which you set the f-stop and the shutter speed is automatically set to a speed that complements the chosen f-stop. "Shutter Priority" is the reverse mode in which you set the shutter speed and the f-stop is set automatically. So, lens speed refers to the maximum aperture―or f-stop―to which your camera lens can open up, and the "faster" the f-stop, the easier it is to shoot under low light and freeze fast-moving subjects. Another lesser-known benefit of fast lenses is that the wider the maximum aperture, the more responsively your camera's autofocus system will perform, especially in lower lighting. Ditto the camera's metering system.
Enough tedious arithmetic. Try these f-stop fun and games: (1) You can use f-stops to determine your camera's dynamic range, at least as displayed on the histogram. Shoot a white wall at one-stop intervals, and check how many stops it takes to shift the values from one edge to the other. That's the dynamic range your histogram will display (see figure). (2) Usually changing the diaphragm by one stop either halves or doubles exposure. But not necessarily for the first two stops on your lens. For example, if your wide-open stop is f/1. 8 and the next stop is f/2. 8, the squares are 3. 24 and 7. 84, which is not a factor of two. (3) Different lenses may give different exposures even with the same f-stop because some have more glass elements than others, causing different amounts of light absorption. That's why cinema lenses (where consistency of exposure is more important) are often marked in T-stops. These are calibrated to exactly produce the same exposure at each stop for different lenses.
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This also means that not all f/1. 2 lenses are created equal. For example The Canon 50mm f/1. 8 has a t-stop of 2. 1, while the Nikon 50mm f/1. 8 has a t-stop of 2. If all of that seems a bit confusing, the video at the top by Matt Granger does a good job of explaining the process in detail. So, whether you're just looking for more knowledge or plan on going lens shopping soon, it's well worth the watch. And if you'd like to see what the F stop to T stop ratio is on the glass in your bag, head on over to DxO Mark.