It’s all the astronomers’ fault

Our photographic consultant is reminded how complicated things are for beginners, no matter how straightforward it all seems to the professionals.

Our photographic consultant was scheduled to give a workshop for beginners last month and so sat down to outline the subjects to cover.  One of these is f-stops, the system that designates how far open a lens is.  On any camera you’ll find a string of numbers, containing 3.5, 4, 5.6, 8, 11, 16 and possibly more at either end.  One point of confusion is that the lens is more open, letting in more light, as the numbers get smaller.

Having numbers get smaller as things get brighter?  It sounds like something astronomers would do (as we mentioned last week).  And putting their heads together, our astronomer and our photographer decided it’s the astronomers’ fault again.

In the days before photography, the major users of imaging lenses were astronomers.  For them there were two important numbers: the diameter of a lens, which told you how much light it could gather; and the focal length, which told you how big the eventual telescope was going to be.  The ratio of these turns out to be important in lens design.  So astronomers would say, ” a six-inch lens of fifteen diameters’ focus,” or 6″ f/15.  A moment of mental arithmetic would give the focal length as seven and a half feet, if you needed the number explicitly.

So when photography came along, lenses that would produce high-quality images were already in existence.  For photographs the focal length was more important than the diameter, so they’d ask for (say) “an f/8 lens of six inches focus,” but the same system applied.

But sometimes, especially as the photographic emulsions got better and faster, they’d want to control the amount of light coming through the lens.  Using either holes cut in a metal sheet or an iris diaphragm they’d reduce the diameter of the part of the lens that was sending light through to the glass plate.  Now, rather than come up with a system like, “my f/8 lens of six inches focus stopped down to one-quarter light,” they treated the working diameter of the lens as a lens in its own right, calling it an f/16 lens.  It’s still the ratio of diameter to focal length, but since the focal length is staying the same while the diameter is getting smaller, the f-ratio is getting larger.  And since the amount of light coming through is proportional to the area, and the area is proportional to the square of the diameter, doubling the f-ratio gives one-quarter of the light.  To cut the light by one-half you multiply the f-ratio by the square root of two (which, rounded off a bit, gives the strange numbers you see on your camera).

Wait–why are we cutting light down by a half and then to a quarter?  Isn’t that rather drastic?  You don’t drive by doubling or halving your speed, or cook by doubling the time in the oven!

It’s in your perception.  Make up a series things in apparently even steps of brightness or darkness, with paint or whatever medium you like.  They’ll turn out to be in even ratios of brightness.  The photographers work with factors of two; depending on the film (or other medium) they can fit in about ten factors, ten “stops,” between dense black and bright white.

So for historical and perceptual reasons we’re stuck with this strange system of f-stops.  But it could have been worse.  If the photographers had taken over the astronomers’ system of magnitudes (see last week’s post), stops would have had a factor of about 2.51, the fifth root of 100.  I leave it to your imagination to work out what the numbers on your camera would look like then.