Results 1 to 2 of 2

Math Help - Optimization Problems - Illumination

  1. #1
    Newbie
    Joined
    Nov 2007
    Posts
    6

    Optimization Problems - Illumination

    Need help on the illumination problem, i have no idea where to start. Any help would be appreciated and thx in advance

    Illumination
    The illumination from a light source is directly proportional to the strength of the source and inversely proportional to the square of the distance from the source. Two light sources of intensities I1 and I2 and d units apart. What point on the line segment joining the two sources has the least illumination?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Eater of Worlds
    galactus's Avatar
    Joined
    Jul 2006
    From
    Chaneysville, PA
    Posts
    3,001
    Thanks
    1
    The light at some point 'a' units from L1 could be represented by:

    k\frac{L_{1}}{d^{2}}+k\frac{L_{2}}{(d-a)^{2}}

    Now, differentiate:

    \frac{dL}{da}=\frac{-2kL_{1}}{a^{3}}+\frac{2kL_{2}}{(d-a)^{3}}

    Now, set to 0 and solve for a.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. illumination problem
    Posted in the Calculus Forum
    Replies: 1
    Last Post: March 9th 2010, 04:13 AM
  2. need help with optimization problems!
    Posted in the Calculus Forum
    Replies: 2
    Last Post: October 5th 2009, 09:48 AM
  3. Optimization Problems
    Posted in the Calculus Forum
    Replies: 0
    Last Post: October 27th 2008, 04:13 PM
  4. optimization problems
    Posted in the Calculus Forum
    Replies: 9
    Last Post: March 24th 2007, 11:35 PM
  5. Replies: 4
    Last Post: November 3rd 2006, 10:14 PM

Search Tags


/mathhelpforum @mathhelpforum