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Math Help - intensity of beam of light

  1. #1
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    intensity of beam of light

    i have a tricky question here, i hope am putting it in the correct section.

    the intensity (I) of a beam of light after passing through a material is given by the formula ( i did it as an attachment so look at it please)

    where k is the initial intensity
    T is the thickness of the material in cm
    c is the absorbtion constant
    if the value of c = 0.0101, at what depth will a vertical beam of light be reduced to 50% of its initial intensity.
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  2. #2
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    At the depth T, intensity I = k/2.
    So k/2 = 4^-cT*k
    2 = 4^cT
    ln(2) = cT*ln(4)
    Now solve for T.
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  3. #3
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    This is more of a question of what value of T will make 1/4^{cT} will generate 1/2. Or in other words, what value of T we need to cut 4 in half. Since 4^{cT} is equivelant to (4^c)^T, we can set up a log equation.

    So since (4^c)^T = 2, then log_{4^c}(2) = T
    Last edited by macosxnerd101; April 9th 2010 at 09:55 PM.
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  4. #4
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    i think i know it would come to a log but am afraid am a bit confused on solving it. and which one of the approach am i suposed to take?
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  5. #5
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    Try them both and see which you prefer. My approach is from the definition of a logarithm. That is:
    <br />
x = b^y<br />
\log_b(x) = y<br />

    The approach sa-ri-ga-ma took is basically the same thing with a change of base formula thrown in.
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