Solving for Volume and Mass Absorption Coefficients in Foggy Astrophysics Class

In summary, the problem involves a row of isotropically emitting streetlamps with an observer standing next to the 1st light. The radiation flux from the 2nd light is 5.0 times that of the 3rd light and the last streetlamp seen is the 12th. The question is to determine the volume and mass absorption coefficients, given an air and fog density of 1.20x10^-3 g/cm^3. Using the equation dIv/ds = -kvIv, the values for k were found to be 0.001073 (1/cm) for volume absorption and 0.89 cm^2/g for mass absorption. However, these values may not be
  • #1
stuffy
32
0
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[/SIZE]

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[/SIZE]
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?
 
Physics news on Phys.org
  • #2
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.
 
  • #3


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.
 

FAQ: Solving for Volume and Mass Absorption Coefficients in Foggy Astrophysics Class

What is Astrophysics?

Astrophysics is a branch of physics that deals with the study of the physical properties and phenomena of objects and matter in the universe. It combines concepts from both astronomy and physics to understand the nature of celestial objects, their interactions, and the laws governing them.

Why is it important to study Astrophysics?

Studying astrophysics helps us gain a better understanding of the universe and its origins. It allows us to answer fundamental questions about the nature of space, time, matter, and energy. It also has practical applications, such as developing new technologies and methods for space exploration and communication.

What topics are covered in an Astrophysics class?

An Astrophysics class typically covers topics such as celestial mechanics, stellar structure and evolution, cosmology, and the properties of galaxies and other celestial objects. Students will also learn about the tools and techniques used in astrophysics research, such as telescopes and spectroscopy.

What skills are needed to succeed in an Astrophysics class?

Success in an Astrophysics class requires a strong foundation in mathematics and physics. Students should also have good critical thinking and problem-solving skills, as well as a strong interest in astronomy and the universe. Good communication skills are also important for presenting research and collaborating with others.

Can I pursue a career in Astrophysics with a degree in this field?

Yes, a degree in Astrophysics can lead to various career opportunities, such as research positions in universities or government agencies, data analysis for space missions, or working in the private sector developing new technologies for space exploration. Many astrophysicists also continue their education and pursue graduate studies in a specific area of astrophysics.

Hot Threads

Recent Insights

Back
Top