Graph of inverse square law for radiation intensity

  1. If I=s/4pir2 would It be correct to write this in terms of logs like this:. lnI=(lns/4pi)-2.lnr Also how could this relate to y=mx+c? I think it's y=lnI. X=lnr. -m= -2 and c= lns/4pi. Is this correct? Thank you
     
  2. jcsd
  3. cepheid

    cepheid 5,194
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    Chegg
    If you meant [itex] \ln I = \ln(S/4\pi) - 2 \ln r [/itex], then yes, this is correct, because

    ln(abc) = ln(a) + ln(bc) (the log of a product equals the sum of the logs of the individual factors in the product).

    and

    ln(bc) = cln(b)

    That looks right. I mean, y is the dependent variable (in this case log of intensity), x is the independent variable (in this case log of radial distance) . The slope m is the constant factor that multiplies the independent variable. The intercept c is what you get when x = 0.

    EDIT: It should be m = -2, NOT -m = -2.
     
    Last edited: Jun 14, 2011
  4. ehild

    ehild 12,267
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    You wrote -m=-2 which results m=2, a positive slope of the ln(I)-lnr graph. Is it right?


    ehild
     
  5. Ah of course it's not -m, seems like I confused myself. Thank you
     
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