Graph of inverse square law for radiation intensity

1. Luke1121

13
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. cepheid

5,194
Staff Emeritus
If you meant $\ln I = \ln(S/4\pi) - 2 \ln r$, 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
3. ehild

12,091
You wrote -m=-2 which results m=2, a positive slope of the ln(I)-lnr graph. Is it right?

ehild

4. Luke1121

13
Ah of course it's not -m, seems like I confused myself. Thank you