Doug Kerr
Well-known member
One may wonder why the measure of the "taking aperture" we know as the f-number (the ratio of the focal length of the lens to the diameter of the aperture) is seen as one of the pivotal parameters of exposure. It might seem that the diameter of the aperture itself (or perhaps its area) would be a more apt parameter. It would seem to be that which determines, from a given small scene region of a certain luminance,, how much luminous flux is gathered by the camera.
In fact, the parameter we quantify with the f-number is known in formal photographic photometrics as the relative aperture. And indeed it is: the ratio of the diameter of the aperture to the focal length of the lens (although upside down).
Here is a homey explanation. Indeed, as to the light from a given small region of a certain luminance, the amount of luminous flux admitted through the lens is proportional to the area of the aperture (that is, to the square of its diameter).
But what is ultimately of importance to the creation of the image is the illuminance caused on behalf of that region on the film or digital sensor. That is the ratio of the amount of luminous flux striking the focal plane on behalf of that region to the era over which it is spread.
As I mentioned just above, indeed the amount of luminous flux is proportional to the square of the diameter of the aperture. But the area over which it is spread on the focal plane is proportional to the square of the distance from the lens to the focal plane.
If we assume a subject at "infinite distance", as we typically do in this matter, then the distance from the lens to the focal plane is the focal length of the lens.
Thus the illuminance on the focal plane is proportional to the square of the ratio of aperture diameter to focal length. So if we know that ratio we can make the needed phtometric calculations–we need not know the actual diameter of the aperture.
For various historical reasons, we actually speak of the inverse of that ratio–the f-number.
Best regards,
Doug
In fact, the parameter we quantify with the f-number is known in formal photographic photometrics as the relative aperture. And indeed it is: the ratio of the diameter of the aperture to the focal length of the lens (although upside down).
Here is a homey explanation. Indeed, as to the light from a given small region of a certain luminance, the amount of luminous flux admitted through the lens is proportional to the area of the aperture (that is, to the square of its diameter).
But what is ultimately of importance to the creation of the image is the illuminance caused on behalf of that region on the film or digital sensor. That is the ratio of the amount of luminous flux striking the focal plane on behalf of that region to the era over which it is spread.
As I mentioned just above, indeed the amount of luminous flux is proportional to the square of the diameter of the aperture. But the area over which it is spread on the focal plane is proportional to the square of the distance from the lens to the focal plane.
If we assume a subject at "infinite distance", as we typically do in this matter, then the distance from the lens to the focal plane is the focal length of the lens.
Thus the illuminance on the focal plane is proportional to the square of the ratio of aperture diameter to focal length. So if we know that ratio we can make the needed phtometric calculations–we need not know the actual diameter of the aperture.
For various historical reasons, we actually speak of the inverse of that ratio–the f-number.
Best regards,
Doug
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