1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Minimize illumination

  1. Apr 28, 2013 #1
    1. The problem statement, all variables and given/known data
    The illumination of an object is directly proportional to to the strength of the source and inversely proportional to the distance squared. If two light sources, one three times stronger than the other, are placed 10 ft apart, where should and object be places on the line between the sources so as to receive the least illumination?

    2. Relevant equations

    -----

    3. The attempt at a solution

    I = s / d^2

    [S/d^2] + [3S/(10-d) ^2] = I <-- minimize

    I'm completely stuck here. Am I treating d as a constant and just doing d/dS or what?

    Sorry that's confusing. I should call distance X instead. Am I taking the derivative with respect to distance was what I meant to ask.
     
    Last edited: Apr 28, 2013
  2. jcsd
  3. Apr 28, 2013 #2

    LCKurtz

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    Yes, it would be better to call the distance from one source ##x## and the other ##10-x## to not confuse it with the ##d## in derivatives. So you have ##I## as a function of ##x##. You have left out the constant of proportionality, which shouldn't matter anyway. So use calculus to find what value of ##x## gives the minimum value of ##I(x)##.
     
    Last edited: Apr 28, 2013
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Minimize illumination
  1. Illumination Problem (Replies: 3)

  2. Minimal Optimization (Replies: 4)

  3. The minimal polynomial (Replies: 2)

  4. Minimal polynomial (Replies: 3)

Loading...