How high above the table should the lamp be placed to achieve maximum

R

Ryan

New member
illumination at the edge of the table? A lamp is suspended above the center of a round table of radius 5 feet. How high above the
table should the lamp be placed to achieve maximum illumination at the edge of the table?
[Assume that the 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 l from the light
source.] Hint: Keep in mind what is constant and what is not. Also what are
you trying to maximize?
 
I = k cos(?) / d²

d² = y² + r²,

cos(?) = y / ?(y² + r²),

I = k [y /?(y² + r²)][1/(y² + r²)] = ky / (y² + r²)^3/2

Now, set dI/dy = 0, and solve for the height, y.

Hope this helps!
 
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