Solving for Volume and Mass Absorption Coefficients in Foggy Astrophysics Class

[stuffy]

Here is the problem...

Consider a row of isotropically emitting streetlamps 15m apart. On a foggy light, an observer standing next to the 1st light notes the radiation flux from the 2nd light is 5.0 times that of the 3rd. The last streetlamp definitely seen is the 12th.
If the air+fog density is 1.20x10^-3 g/cm^3, what are the volume and mass absorption coeff?

This is my work so far...

F2 = 5F[SIZE]3

Using the equation dIv/ds = -kvIv
I set Iv=Fv (Intensity = flux)
therefore dFv/Fv = -kvds
Integrating the left side from F2 to F3, the right hand side from 0 to s.
I got ln(F3/F2) = -ks, where F2 = 5F[SIZE]3
so k = -ln(1/5) / s, where s = 15m

here i got that k = .001073 (1/cm) for volume absorption coeff
and 0.89 cm^2/g for the mass absorption coeff...

They don't seem right, can anyone give a better direction?

 

[stuffy]

No takers?

According to my calculations, the 2nd streetlap is about 9 million times "brighter" than the 12th. Optical depth of the 2nd lamp is around 1.7, 12th about 18.

 

[wais]

Your work so far seems to be on the right track. However, there are a few things to consider in order to get more accurate results.

Firstly, the equation you are using, dIv/ds = -kvIv, is the Beer-Lambert law, which relates the intensity of light to its absorption coefficient and the distance it travels through a medium. This law assumes that the medium is homogeneous, meaning that the density and composition of the medium do not change along the path of the light. In this case, the fog density is given, but it is important to note that fog is not a homogeneous medium. It is made up of tiny water droplets that scatter and absorb light in a non-uniform manner. This can affect the accuracy of your results.

Secondly, the equation you have used assumes that the light from the streetlamps is isotropic, meaning that it is emitted in all directions equally. However, in reality, streetlamps emit light in a specific direction, which may not be isotropic. This can also affect the accuracy of your results.

To improve your results, you could try using a more accurate equation for light absorption in fog, such as the Mie scattering equation, which takes into account the non-uniform nature of fog particles. Additionally, you could try taking measurements at different distances from the streetlamps and averaging your results to account for any directional emission of light.

Overall, solving for volume and mass absorption coefficients in foggy astrophysics class can be a challenging problem due to the complex nature of fog as a medium. It is important to consider the limitations of the equations and assumptions made in order to get more accurate results.