Calculus

posted by .

"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 strong as the other. Where is the darkest spot between the two lights?"

I can draw the diagram, and can organize all the information, but can't seem to bring it all together into an equation I can work with.

  • Calculus -

    Distance between street lights, L = 40m
    Distance of darkest point from left light = x
    Distance of darkest point from right light (twice as strong) = L-x
    Height of street light from ground in metres
    = h

    Assuming
    1. The right light is twice as strong as the left, and
    2. the "darkest" point is located along a straight line joining the two lights.

    Illumination by left light, I1
    = K/(h²+x²) K=light constant
    Illumination by right light, I2
    = 2K/(h²+(L-x)²)

    Total illumination, I
    = I1+I2
    =K/(h²+x²)+2K/(h²+(L-x)²)

    Differentiate with respect to x and equate to zero and solve for x (in terms of K and h) to find the minimum luminosity.

    I get 17.7 m from the weaker light, assuming the height above ground h=0.

  • Calculus -

    Oh I see! Thank you!

  • Calculus -

    A street light is at the top of a 19 ft tall pole. A woman 6 ft tall walks away from the pole with a speed of 5 ft/sec along a straight path. How fast is the tip of her shadow moving when she is 40 ft from the base of the pole?

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. 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 …
  2. 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 the …
  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 …
  4. 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 74.0 …
  5. 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 74.0 …
  6. Math

    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 74.0 …
  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 were …
  8. 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 were …
  9. 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 other, …
  10. 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 …

More Similar Questions