if the illumination of an object is directly proportional to the strength of its ligth source and inversly proportional to the square of the distance in between it and that particular ligth source then find out the formula that would calculate the amount of illumination on an object that is between two lamps , one twice as strong(brigth) as the other and the distance between them is 40 m .
then find out what would be the darkest position between those two lamps?
p.s its not reall an engineering question but if your in the faculty of engineering id assume its easy for you
2007-04-01 15:37:40 · 1 answers · asked by morgan 2 in Science & Mathematics ➔ Engineering
L1 = L0/R1^2
L2 = 4L0/R2^2
Lt = L1 + L2
Lt = L0/R1^2 + 4L0/(40 - R1)^2
dLt/dR1 = -2L0/R1^3 + 8L0/(40 - R1)^3
The intensity will be a minimum when
2(40 - R1)^3 = 8R1^3
2(64000 - 4800R1 + 120R1^2 - R1^3) = 8R1^3
10R1^3 - 120R1^2 + 9600R1 - 128000 = 0
R1^3 - 12R1^2 + 960R1 - 12800 = 0
R1 = 15.45952838 m
2007-04-01 17:15:04 · answer #1 · answered by Helmut 7 · 0⤊ 0⤋