In the last part, I had a look at the influence of the incident illumination angle. To prevent the post from getting too long, I essentially skip the explanation why that is.
However, since this is one of the more important things to the sunny 16 rule, I would like to pick up the topic once again.
The basic principle behind the angle of incident light can be illustrated by the phases of the moon.
Please have a look, e.g. on this web-page.
0˚ between illumination and line of sight
If the sun is directly behind us, and the moon is directly in front of us, that would be full moon. In this phase we all the sunlight shining on the moon.
If the sun is on either side of us, this happens during the first and third quarters of the moon, very obviously, we see only half the light illuminating the moon.
In terms of photography, reducing the amount of illumination by half reflects 1 f-stop. To compensate for this lost stop, we need to open the aperture by one stop, or double the exposure time.
When we are actually looking into the light source, the analogy to the phases of moon starts to become a little weak. The reason for that is, that we can't see any of the sunlight illuminating the moon, still the moon is somewhat visible, due to earth-shine. Earth-shine is the sunlight that the earth reflects, which then illuminates the moon. As I said, this is when the analogy phases out.
However, we still can learn something about illumination of a scene in photography.
In earth, we are surrounded by an atmosphere, which itself scatters light. This scattered light is the illumination of a scene shot under backlit conditions. Of course, scattered light is less intense than direct light. To compensate for this, we need to further open the aperture.
This, of course, only holds true if details of a scene are to be photographed. For a backlit profile photo, the exposure has to be set to match the brightness of the light source, i.e. stopping down the exposure, rather than open it up.