Cameras and Lenses
F-stops, Focal Length and Lens Aperture
The focal length of a lens is the distance between the optical center of the lens and the film plane (for film cameras) or CCD (for camcorders). The longer the focal length, the more it “magnifies” the subject.
when referring to the numeric value of your lens aperture, you will find it described as an f-stop. The f-stop is one of those old photography terms that, technically speaking, relates to the focal length of the lens (e.g., 200mm) divided by the effective aperture diameter.
f-stop = focal length / diameter of lens opening
Thus a 50mm lens with an iris diameter of 25mm has an aperture of 50 / 25 = f2.0
These measurements are defined as “stops” and work incrementally with your shutter speed to determine proper exposure. Older camera lenses used one-stop increments to assist in exposure adjustments, such as 1.4, 2, 2.8, 4, 5.6, 8, 11, 16, and 22. Each stop represents about half the amount of light entering the lens iris as the larger stop before it. Hence f2.0 is a wide aperture, whereas f11.0 is a narrow aperture.
Today, most lenses don’t have f-stop markings since all adjustments to this setting are performed via the camera’s electronics. The stops are also now typically divided into 1/3-stop increments to allow much finer adjustments to exposures, as well as to match the incremental values of your camera’s ISO settings, which are also adjusted in 1/3-stop increments.
Reducing the f-stop of a lens (increasing its aperture) has three effects:
The relationship between f-stop and exposure is not linear. If you open the iris of the lens by one stop, you are doubling the amount of light that goes through. Conversely, reducing the aperture by one stop halves the exposure (other things being equal). Opening the iris by two stops increases the exposure by a factor of four, opening it by three stops brightens the image by a factor of eight, and so on.
This explains the standard sequence of f-stops shown above, which may seem arbitrary, but in fact makes perfect mathematical sense: since it is the area of the lens opening that determines how much light goes through, to double the area we must divide the f-number by the square root of 2, which is approximately 1.414 – hence the weird numbers. (This is because area is proportional to the square of linear dimensions.)
You can check this yourself by verifying that to go from an f-stop to one of its neighbors you multiply or divide by approximately 1.414.
Mathematical considerations aside, the thing to remember about f-stops is that they refer to lens aperture relative to focal length, and that they are also used to refer to the illumination of a subject: if we say an actor’s face is one stop underexposed, it typically means that we should double the illumination of the actor’s face – we should add one stop’s worth of lighting to it.
As noted above, the vale of the f-stop depends on the apparent diameter of the lens. The apparent aperture diameter depends on the magnification of the lens. For example, an aperture that is 50mm wide might look 100mm wide as a result of the lens elements in front of it; the apparent diameter of the iris diaphragm is what matters when calculating F-stops.
This means of course that when you zoom in (increase the focal length of the lens), the apparent aperture increases, since it is being magnified. However, since the value of the f-stop is the ratio between focal length and apparent aperture, the f-stop also stays approximately constant.
Zoom lenses are designed in such a way that when you zoom in or out, the change in focal length exactly compensates the change in the apparent aperture. Hence there is no difference in exposure when you zoom in or out.
In practice, even the best lenses exhibit light absorbance, effectively “stealing” some of the light going through them. This means that if you calculate the exposure based on the f-stop of the lens, you will end up underexposing the image, because less light is reaching the film plane than is expected in theory. T-stops are the f-stop of the lens corrected for its absorbance and reflectance. The T-stop is the true speed of the lens, calculated by compensating for its light absorbance and reflectance, and will result in accurate exposure.
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