During a solar eclipse, the sky maintains a high brightness even when the Sun is, say, 95% eclipsed by the Moon. During the last ten seconds before totality is when most of the darkening of the sky occurs.
How can you predict the apparent brightness of the sky as the Moon eclipses the Sun? You may assume there are no clouds in the area.
Related Question:
An important point is that our perception of brightness is approximately logarithmic, so each halving of the light is perceptually the same. The sky is not totally dark at totality, so you might model the apparent brightness as $\log (x+a)$ where $x$ is the fraction of the solar disk exposed and $a$ is the brightness at totality. $a$ will be much smaller than $1$, so the step from no coverage to half coverage will be the same as the step from half to quarter, and probably for another few steps before $a$ starts to matter. Now you have to find a function of time that gives the fraction of the solar disk that is covered.
