Stop, Just Stop!

Our eyes and ears have logarithmic responses. That is to say that we respond naturally to twice the light intensity, or twice the pitch of a sound, or twice the volume.

This explains the octave in music. The same goes for the eye.

A stop in photography represents a doubling of the light.

Memorize this.

Now recall the basic equation:

Luminous Energy ∝ L × r² × t

As a general rule, L is what it is. Whether you have a brightly lit garden, or a candlelit dinner, you have no control over it. What you can control however are r and t. So what would it take to double the light?

Well, you can either double the time, or increase the radius by √2.

If you understand this, you will understand the f-stop system which goes as 1.0, 1.4, 2, 2.8, 4, 5.6, etc. They are each increasing by exactly √2. (If you don't understand this statement, we will go into the f-stop stuff in gory detail later.)

Many many photographers do not grasp this. How a stop represents both increasing time, or dialing "down" the aperture. Is it time, or is it aperture?

The answer is both! You increase total light energy by letting more in.

Let there be light!

In the beginning, there was light.

Imagine a very bright source of light which is perfectly monochromatic (just one wavelength.)

Imagine you are in the room next door with a pinhole looking at it. (like the movie Psycho.)

The number of photons streaming past you is proportional to the intensity of the light (how "bright" it is), the size of the pinhole, and the length of time that you look.

Let's assume the pinhole is circular. (This will not really matter, as you will see later.)

In physics, instead of measuring the number of photons of a monochromatic source, it's simpler to measure their total energy because they are proportional. (E = h × ν.)

Illuminance is basically the amount of energy that is pumped out per unit area of the source.

(Aside: it's a little more complicated for light that is not all of the same color but let's ignore this point just for the time-being. We will return to this point later.)

Let L be the illuminance. If the pinhole is perfectly round and has radius r, and you look for time t.

Luminous Energy ∝ L × r² × t


That symbol (∝) which stands for "proportional" refers to the fact that the two quantities are related with a hidden constant — in this case, π, if you want to get all technical.

This should be very very intuitive. Double the illuminance (energy) pumped out, and well, you get double the energy (DUH!)

Double the time, and twice as many photons stream past.

Increase the radius, and the area increases as the radius-squared. This is the only tricky part.

Memorize this stuff. Everything that follows will be a direct consequence of this formula.

That pesky little "square" of the radius will play a disproportinate role in what follows. Take a careful note of that little bastard!