To obtain an exposure, a lens must be controlled through its aperture, just like the iris of the human eye. "In bright-light situations, the iris is dilated to reduce the size of the pupil and limit the amount of light which enters the eye; and in dim-light situations, the iris adjusts its size so as to maximize the size of the pupil and increase the amount of light which enters the eye"2
The lens aperture controls the amount of light it transmits to the film or sensor plane, by adjusting the size of the opening in the lens diaphragm. The relative size of such aperture openings is represented by f-numbers, called apertures or f-stops.
The actual diameter of the aperture can be calculated by dividing the focal length over the f-stop value. The apertures are shown below for a 50mm f/1.4 Nikkor lens, as well as the actual diameters of each one.
The f-stop numbers follow a rounding figure convention for the sake of engraving aperture rings, now useful in LCD displays. Since each full f-stop number was established to progressively allow for twice as much light transmission as the next larger one, true f-stop values are multiples of the square root of 2 or 1.4142 as follows:
To illustrate what the apertures really mean for light transmission, lets imagine a situation where 100% of light would be transmitted at f/4, twice as much light will be transmitted one f-stop under or f/2.8, half of that light will be transmitted one stop above or f/5.6, and so on as shown in the table below:
F-Stop and Shutter Speed
How long we let such transmitted light hit the film or sensor is the second control variable for exposure: shutter speed. The following table shows equivalent exposures, as combinations of f-stop values and shutter speeds in fractions of a second, considering a sensitivity of ISO 100 under bright light conditions in open shade:
What is important of the exercise above is that: for a given exposure, each one more full stop "down" (smaller in diameter) requires twice longer the shutter speed of the previous one. For each one more full stop "up" (bigger in diameter) to achieve the same exposure requires half longer the shutter speed than the stop before.
You can now select an equivalent shutter speed-aperture combination to suit your needs. If the subject is moving you will need a combination with a high shutter speed. If you want maximum depth of field, you may choose a very small aperture (higher f-stop number) with a good tripod to allow for slow shutter speeds.
A typical lens usually performs better wehen at f/8 and f/16. High-end pro glass performs equally well wide open at its maximum aperture than when stopped down.
F-Stop, Size of Glass and Cost
The wider the aperture of a lens is, the faster it can shoot when wide open (at its smallest f/stop number), the larger the glass, the higher its materials and manufacturing costs and therefore its price. For available dim light photography a "fast" lens is required.
How wide is widest possible depends on the focal length and the complexities and feasibility of manufacturing such lens. A 50mm f/1.8 lens has an effective diaphragm aperture of 50mm/1.8 = 27.8 mm (1.1") of diameter; a more manageable size than that of a 600mm f/4 that has a diameter of 150 mm (5.9"). This lens, to be a f/1.8 would need an effective diaphragm aperture of 600/1.8 = 333 mm (12.1"), a very wealthy person to order it and one strong pack mule or two to carry it.
A lens is known as a "pro" lens when it is "fast", has been corrected for all kinds of possible aberrations and it is built to last a lifetime, provided we don't drop it.
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