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!

Minimization of Illumination

  1. Oct 27, 2015 #1
    1. The problem statement, all variables and given/known data
    Two light sources of identical strength are placed 8 m apart. An object is to be placed at a point P on a line ℓ parallel to the line joining the light sources and at a distance d meters from it (see the figure). We want to locate P on ℓ so that the intensity of illumination is minimized. We need to use the fact that the intensity of illumination for a single source is directly proportional to the strength of the source and inversely proportional to the square of the distance from the source.

    4-7-74.gif

    (a) Find an expression for the intensity I(x) at the point P. (Assume the constant of proportionality is 1.)

    (b) If d = 4 m, use graphs of I(x) and I'(x) to find the value of x that minimizes the intensity.

    (c) If d = 8 m, find a value of x that minimizes the intensity.

    (d) Somewhere between d = 4 m and d = 8 m there is a transitional value of d at which the point of minimal illumination abruptly changes. Find this exact value of d.

    2. Relevant equations


    3. The attempt at a solution
    I'm not sure how to approach the problem at first glance. I started by writting dow this for (a):
    [tex] I(x)= \frac{1}{d^2}[/tex]
    I'm pretty sure I'm wrong with this. I just need enough to get me started.
     
  2. jcsd
  3. Oct 27, 2015 #2

    Samy_A

    User Avatar
    Science Advisor
    Homework Helper

    ##I(x)## should depend on (the square of) the distance of the object to each of the two lamps.
     
  4. Oct 27, 2015 #3

    Mark44

    Staff: Mentor

    That should be the reciprocal of the distance squared. As you have written it above, the intensity would be greater for longer distances.
     
  5. Oct 27, 2015 #4

    Ray Vickson

    User Avatar
    Science Advisor
    Homework Helper

    I(x) is NOT 1/d^2, because 1/d^2 does not depend at all on x---so no matter where you locate P, the illumination would be unchanged. Does that sound right to you?

    Hint: go back and re-read the question in detail; make sure you pay attention to every single word!
     
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: Minimization of Illumination
  1. Illumination Problem (Replies: 3)

  2. The minimal polynomial (Replies: 2)

  3. Minimize illumination (Replies: 1)

  4. Minimal polynomial (Replies: 3)

Loading...