What is the illuminance (in lm/m^2) on a desktop if the lamp is 0.9 m above it? The equation of the illuminance, E, of a small light source is   E = P/ 4(pie)d^2, where P is the luminous flux (in lumens, lm) of the source and d is its distance from the surface. Suppose the luminous flux of a desk lamp is 1200 lm.  Name the values of d if any that are not in the domain of the given function.  

Expert Answers

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Rearranging terms, E ( 4(3.1416)d^2 ) = P, so

E ( 4(3.1416)[.9m^2] ) = 1200 lm

E ( 12.57 [.81m^2] ) = 1200 lm

E (10.17m^2) = 1200 lm

E = 1200 lm / 10.17 m^2

E = 118 lm/m^2

 

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