Using line intensity ratios to determine the geometry of plasma in stars via their apparent areas

A simple method of calculating the mean line of sight in solid figures is demonstrated and used in conjunction with the Cauchy theorem for the mean chord. This gives a straightforward expression for the enhancement ratio of a uniform optically thick plasma as four times the ratio of the area of the shadow of the plasma in the line of sight to the full surface area. This is used to deduce that the maximum value this enhancement can take is two. The method is used in the analysis of a sphere and cylinder, and shows that the ratio can be calculated exactly for any angle of observation in these cases. This ratio is linked to its applications in the study of opacity effects in the plasma of distant stars, in particular the use of spectral line intensity ratio enhancement observations to make inferences about plasma geometry.