A light source is placed on a table at a distance d
from the center of a coin.
The illumination of the coin is poor due to the low angle of illumination.
Lifting the light above table's level will improve the angle, but increase the distance.

What is the height needed to get the best illumination of the coin?

N.B. The puzzle was not placed in the "Calculus" category.

There is a problem in the lack of definitions of terms used in this puzzle. 'Illumination' and 'angle of illumination' are not  mathematical terms. And an important question is: what is the criteria for judging 'best'?
If the problem were to be addressed in physics, the size of the 'sphere' of illumination (in order to calculate the steradian) and the  surface area of the coin being illuminated (or such that it can be calculated) would seem to be needed [an assumption is made that the coin is to be treated as perfectly flat and in the same plane as the table, also having no 'thickness'] -- in addition to being provided the answer to the question forementioned. 

Posted by Dej Mar on 2016-07-06 14:25:31