1. Limited time only! Sign up for a free 30min personal 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!

Homework Help: Differentiation problem

  1. Oct 3, 2004 #1
    hi, could anyone guide as to how to go about solving this question?
    A cicular patch of grass or radius 20m is surrounded by a walkway and a light is placed atop a lamppost at the circle's center. At what height shoud the light be placed to illuminate the walkway most strongly? The intensity of illumination "I" of a surface is given by
    I = [k.sin(theta)] / D^2 where is the distance from the light source to the surface and theta is the angle at which light strikes the surface, and k i s a positive constant

    pls anyone, just give me a push, i am competely cluess as to where to begin.
  2. jcsd
  3. Oct 3, 2004 #2


    User Avatar
    Science Advisor
    Homework Helper

    Just write [itex]\sin \theta[/itex] in terms of D and R (radius of the circle) and set the derivative of I with respect to D equal to 0, etc.
  4. Oct 3, 2004 #3
    [tex] \textrm{Here goes some hints...} [/tex]

    [tex] R = 20 \textrm{ m} [/tex]

    [tex] \hline [/tex]

    [tex] R = D \cos \theta [/tex]
    [tex] h = D \sin \theta = \frac{R}{\cos \theta} \cdot \sin \theta = R \tan \theta [/tex]

    [tex] \hline [/tex]

    [tex] I = k\cdot \frac{\sin \theta}{D^2} [/tex]
    [tex] \sin \theta = \frac{ID^2}{k} [/tex]
    [tex] \frac{h}{D} = \frac{ID^2}{k} [/tex]
    [tex] h = \frac{ID^3}{k} [/tex]
    [tex] h = \frac{I}{k}\left( \frac{R}{\cos \theta} \right)^3 [/tex]​

    [tex] \textrm{Good luck!} [/tex] :smile:
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook