$($a$)$ What is the maximum distance at which one can see a black automobile on a foggy, moonlit night? Assume that the fog consists of $5-$m droplets at $1010/$m$3[104/$cm$3],$ that the background luminance is $10-3$ cd$/$m$2,$ and that your eyes are completely dark adapted, $($b$)$ Repeat part $($a$)$ if the headlights are on and are directed toward you; assume that the inherent contrast is $104.$