# Graph of inverse square law for radiation intensity

• Luke1121
In summary: So yes, the slope m = -2, which results in a negative slope for the ln(I)-ln(r) graph, indicating an inverse relationship between intensity and radial distance. In summary, the conversation discusses the use of logarithms to simplify the equation I = s/4πr^2 and relates it to the equation y = mx + c. It is determined that ln(I) = ln(s/4π) - 2ln(r) is a correct representation, with ln(I) as the dependent variable, ln(r) as the independent variable, and a slope of -2. The conversation also clarifies that the slope should be -2, not 2.
Luke1121
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

Luke1121 said:
If I=s/4pir2 would It be correct to write this in terms of logs like this:. lnI=(lns/4pi)-2.lnr

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)

Luke1121 said:
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

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

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

Yes, it would be correct to write the inverse square law equation in terms of logs as lnI=(lns/4pi)-2.lnr. This can also be related to the equation y=mx+c, where y=lnI, x=lnr, m=-2, and c=lns/4pi. This is because the inverse square law shows a linear relationship between the logarithm of intensity and the logarithm of the distance. So, when plotted on a graph, the data would form a straight line with a slope of -2 and a y-intercept of ln(s/4pi). Therefore, your interpretation is correct.

## 1. What is the inverse square law for radiation intensity?

The inverse square law for radiation intensity states that the intensity of radiation is inversely proportional to the square of the distance from the source. This means that as the distance from the source increases, the radiation intensity decreases by the square of that distance.

## 2. What is the graph of the inverse square law for radiation intensity?

The graph of the inverse square law for radiation intensity is a curve that slopes downward as the distance from the source increases. It starts at a high intensity near the source and gradually decreases as the distance increases, following the inverse square relationship.

## 3. How is the inverse square law for radiation intensity used in science?

The inverse square law for radiation intensity is used in many fields of science, including astronomy, physics, and radiology. It helps scientists understand how radiation dissipates as it travels through space or materials, and is essential in calculating safe exposure levels for various types of radiation.

## 4. What factors can affect the accuracy of the inverse square law for radiation intensity?

The inverse square law for radiation intensity assumes that the radiation is emitted from a single point source, but in reality, most sources emit radiation from a larger surface. This can affect the accuracy of the law. Other factors such as absorption, scattering, and reflection can also impact the accuracy of the law.

## 5. Can the inverse square law for radiation intensity be applied to all types of radiation?

Yes, the inverse square law for radiation intensity can be applied to all types of radiation, including light, sound, and electromagnetic radiation. However, the law may need to be modified for certain situations, such as when the radiation source is not a point source or when other factors significantly affect the intensity of the radiation.

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