math

The illumination of an object by a light source is directly proportional to the strength of the source and inversely proportional to the square of the distance from the source. If two light sources, one three times as strong as the other, are placed 10 ft apart, how far in ft from the stronger source should an object be placed on the line between the sources so as to receive the least TOTAL illumination (the sum of the illumination from each source)?


Let x be the distance from the stronger source, in feet. The distance from the weaker source is therefore (10 - x). Let the total radiant power of the brighter souce be 3P and the other equal to P.

The received illumination is
Y = 3P/x^2 + P/(10-x)^2

Differentiate that to find where dY/dx = 0. Mimimum illumination will be there. You won't need to know P; it will cancel out.

  1. 👍 0
  2. 👎 0
  3. 👁 251

Respond to this Question

First Name

Your Response

Similar Questions

  1. calculus

    The illumination of an object by a light source is directly proportional to the strength of the source and inversely proportional to the square of the distance from the source. If two light sources, one three times as strong as

    asked by robert on June 30, 2009
  2. Math

    The illumination of an object by a light source is directly proportional to the strength of the source and inversely proportional to the square of the distance from the source. If two light sources, one four times as strong as the

    asked by Alex on November 28, 2014
  3. Math

    The illumination of an object by a light source is directly proportional to the strength of the source and inversely proportional to the square of the distance from the source. If two light sources, one four times as strong as the

    asked by Samantha on November 14, 2011
  4. MATH 100

    The illumination of an object by a light source is directly proportional to the strength of the source and inversely proportional to the square of the distance from the source. If two light sources, one 10 times as strong as the

    asked by J on November 27, 2014
  5. Calculus

    "The illumination of an object by 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 streetlights are 40m apart and one is twice as

    asked by Stuck on June 20, 2010
  6. College Algebra

    The illumination produced by a light source is inversely proportional to the square of the distance to the source. If a light source 5m from an object illuminates with 70 candela, what illumination would be produce if the object

    asked by meme on March 21, 2012
  7. Math

    The illumination produced by a light source is inversely proportional to the square of the distance to the source. If a light source 5m from an object illuminates with 70 candela, what illumination would be produce if the object

    asked by Hi on March 20, 2012
  8. Algebra II

    The intensity of illumination at a given point is directly proportional to the intensity of the light source and inversely proportional to the square of the distance from the light source. If a desk is properly illuminated by a

    asked by Ashley on November 22, 2011
  9. Algebra II

    The intensity of illumination at a given point is directly proportional to the intensity of the light source and inversely proportional to the square of the distance from the light source. If a desk is properly illuminated by a

    asked by Marie on November 22, 2011
  10. Algebra II

    The intensity of illumination at a given point is directly proportional to the intensity of the light source and inversely proportional to the square of the distance from the light source. If a desk is properly illuminated by a

    asked by Zach on November 21, 2011

More Similar Questions