The illumination of an object by a light source is directly proportional to the strength of the source and inversely proportional to the square of the distance from the source. If two light sources, one three times as strong as the other, are placed 12 ft apart, where should an object be placed on the line between the sources so as to receive the least illumination?
Give your answer as the distance, in feet, between the object and the strongest light source.
2007-05-13 15:28:51 · 1 answers · asked by miss-whatever1225 1 in Science & Mathematics ➔ Mathematics
The beginning equation is
I(total) = SUM (KSi/ Dsi^2) where K is a constant, Si is the intensity of a source, and Dsi is the distance from the source to the object. Here, we have the two sources on a 12 foot line with the object in-between them. Since we ultimately want Dsh (the strong source distance), we can express Dsw (the weak source distance) as 12-Dsh. Tossing all this stuff in, we have
I(total) = KS ( 3/Dsw^2 + 1/(12-Dsw^2) )
This is the equation for you to take dI(total)/Dsw, set to zero and solve for Dsw.
2007-05-13 15:50:47 · answer #1 · answered by cattbarf 7 · 0⤊ 0⤋