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Math Help - illumination problem

  1. #1
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    illumination problem

    im not understanding how to set this problem up. 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 I(1) and I(2) are d units apart. what point on the line segment joining the two sources has the least illumination? huh? im definitely lost! thanks in advance..
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  2. #2
    MHF Contributor

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    "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"
    So illumination= \frac{k I}{r^2} for some constant k. The illumination from two sources is the sum of the two separate illuminations:\frac{k I_1}{r_1^2}+ \frac{k I_2}{r_2^2}[/tex]


    Let x be the distance from the first light source to a point p on the line between the two light sources: r_1= x. Then the distance from the other light source to p is r_2= d- x.

    The total illumination is \frac{k I_1}{x^2}+ \frac{k I_2}{(d-x)^2}.

    The minimum illumination will be where the derivative of that, with respect to x, is 0.
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