How Do You Apply the Inverse Square Law to Light Intensity?

[kroniic]

Hello all, I am currently in Year 11 (Australia),

1st time posting but I really need help, my Physics teacher did not explain how to use the Inverse Square law when dealing with the intensity of light and to make things worse, he would not help me I have a theory why but that is another story, what I need help with is how to put the Law to use for a report that is due tomorrow. :(

Many Thanks,

Anthony

 

[rcgldr]

Most forms of energy from a point source travel away from the point source in the shape of a sphere, or part of a sphere, such as a sound wave, or a beam of light. Since the area of the sphere is related to the square of the radius of the sphere, which is the distance from the point source, the amount of energy per unit area decreases by the square of the distance from the point source.

For some forces like gravity that effectively eminate from a point source (the center of mass of the object creating the gravitational field if the distance is suffieciently outside the object, depending on how spherical the object is), the amount of force decreases with the square of the distance. The reasoning could be similar to the energy case I stated above, but not all forces follow the inverse square law, for example the strong force that holds the the nucleus of atoms together has a finite distance of effectiveness, while forces that follow inverse square law extend to infinity (they are non-zero forces at any finite distance from the point source).

On a side note, if the energy is eminated from an infinitely long line, the energy per unit area decreases linearly with the distance from the line, and if the energy is eminated from an infinitely large plane, the energy per unit area is constant, the same at any distance from the plane. Gravity would follow the same rules, but the model would be an approximation, such as a very long cylinder, or very large plane with the target point relatively close enough to the line or plane shaped object producing the gravity to act similar to an infinitely long line or infinitely large plane.

 

[kroniic]

Most forms of energy from a point source travel away from the point source in the shape of a sphere, or part of a sphere. Since the area of the sphere is related to the square of the radius of the sphere, which is the distance from the point source, the amount of energy per unit area decreases by the square of the distance.

On a side note, if the energy is eminated from an infinitely long line, the energy per unit area decreases linearly with the distance from the line, and if the energy is eminated from an infinitely large plane, the energy per unit area is the same at any distance from the plane.

I sort of understand it, like how it will be 1/4 of the intesity, there was something my teacher was saying about being directly proportional, indirectly and such, also said something about when plotting it, it will be a straight like rather then a curve.

 

[rcgldr]

Directly proportional usually implies a linear, and not a quadratic relationship. Inverse square is a quadratic relationship, and the shape of the curve is a part of a parabola that extends along the x (distance) axis. (y = sqrt(x), or x = y^2). So if the distance doubles, the intensity at that doubled distance decreases by a factor of 4.

 

[tiny-tim]

… there was something my teacher was saying about being directly proportional, indirectly and such, also said something about when plotting it, it will be a straight like rather then a curve.

(I don't think there's any such thing as "indirectly proportional" - could it have been "inversely proportional"?)

I don't understand how the Inverse Square Law can be directly proportional, or how it can be plotted straight - unless the teacher was talking about logarithms.

 

[Doc Al]

To complement Jeff's explanation, you might want to read this: http://hyperphysics.phy-astr.gsu.edu/Hbase/forces/isq.html#isq"

 

[Lojzek]

(I don't think there's any such thing as "indirectly proportional" - could it have been "inversely proportional"?)

I don't understand how the Inverse Square Law can be directly proportional, or how it can be plotted straight - unless the teacher was talking about logarithms.

Power density plot can be straight if we put 1/r^2 on abscissa axis.
Or maybe the lecture was about amplitude of electric field? Amplitude if electric field is proportional to quare root of intensity, so amplitude is inversely proportional to r=proportional to 1/r.