SOLUTION: A light hangs 4.8 ft above the center of a circular table 7.2 ft in diameter. If the illumination is 25 lux at center of the table, what is it at te edge of the table?

Algebra ->  Customizable Word Problem Solvers  -> Misc -> SOLUTION: A light hangs 4.8 ft above the center of a circular table 7.2 ft in diameter. If the illumination is 25 lux at center of the table, what is it at te edge of the table?      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 328014: A light hangs 4.8 ft above the center of a circular table 7.2 ft in diameter. If the illumination is 25 lux at center of the table, what is it at te edge of the table?
Answer by galactus(183) About Me  (Show Source):
You can put this solution on YOUR website!
There is no constant of proportionately. But, illumination, I, is directly proportional to the cosine of the angle of incidence of the light rays and inversely proportional to the square of the distance from the source.
I=k%2A%28cos%28x%29%2FL%5E2%29
k is the constant of proportionately.
Let h=4.8, the height the light is above the table.
Then, cos%28x%29=h%2FL
L=sqrt%28h%5E2%2Br%5E2%29
So, I=k%2A%28h%2FL%5E3%29=k%2A%28h%2F%28%28h%5E2%2Br%5E2%29%5E%283%2F2%29%29%29
Since the illumination is 25 at the center, then:
25=k%2A%284.8%2F%28%284.8%29%5E2%2B0%5E2%29%5E%283%2F2%29%29%29
k=576
Now, since the edge of the table is at r=7.2 and we now have k
I=576%2A4.8%2F%28%284.8%29%5E2%2B%287.2%29%5E2%29%5E%283%2F2%29=4.27
As I said, I am winging it here since there is no k given. So I am using what I know about light.