Elementary astrophysics - monochromatic flux?

[jeebs]

hi, I am having trouble deriving an expression for converting between monochromatic flux expressed in wavelength and in frequency units.

i think that the monochromatic flux of a star is found by

F(Δf) = ΔE / ΔtΔfΔA

F(Δλ) = ΔE / ΔtΔλΔA

where
E = energy,
t = time,
Δf = frequency bandwidth,
A = area of photon collecting surface, and
Δλ = wavelength bandwidth.

however, I'm not even sure that these equations are correct... if I'm wrong can somebody set me straight?

i was shown how to do this question by my tutor but i can't remember how to do it, it involved differentiation or integration i think...

as far as i have got with this is shortening the energy over time part into power, and rewriting either the wavelength in terms of frequency and c, or vice versa. not very impressive i know.so can you please help, its important that i find out how to do this.

thanks!

oh, and if you take the time to answer, could you please give me an explanation, as the answer itself doesn't really teach me anything, I'm more interested in how you found that answer.

 

[Nate810]

Thanks!The equation you need to use to convert between monochromatic flux expressed in wavelength and in frequency units is the formula for Planck's law:F(Δf) = (2πhc^2)/Δf^5 * [exp(hc/kTΔf) - 1]F(Δλ) = (2πhc^2)/Δλ^5 * [exp(hc/kTΔλ) - 1]where h is Planck's constant, c is the speed of light in a vacuum, k is Boltzmann's constant, and T is the temperature of the star. You can then use algebra to rearrange the equations so that one is expressed as a function of the other. For example, you can use algebra to rearrange F(Δf) to be expressed as a function of Δλ and vice versa. Hope this helps!

 

[Moetasim]

Hi there,

I would be happy to help you with your question about monochromatic flux in astrophysics.

First, let's define what monochromatic flux is. It is the amount of energy per unit time per unit area that is emitted by a source at a specific wavelength or frequency. In other words, it is a measure of the intensity of light at a particular wavelength or frequency.

Now, let's look at your equations. You are correct that monochromatic flux can be calculated using the equation F = ΔE / ΔtΔA, where ΔE is the energy emitted, Δt is the time, and ΔA is the area of the collecting surface. However, you need to consider the bandwidth of the wavelength or frequency in order to get an accurate measurement.

For monochromatic flux expressed in frequency units, the equation is F(Δf) = ΔE / ΔtΔfΔA, where Δf is the frequency bandwidth. This is because the energy emitted can vary over a range of frequencies, and we need to take into account the specific range we are interested in.

Similarly, for monochromatic flux expressed in wavelength units, the equation is F(Δλ) = ΔE / ΔtΔλΔA, where Δλ is the wavelength bandwidth. Again, we need to consider the range of wavelengths in order to get an accurate measurement of the flux.

To convert between the two, we can use the relationship between frequency and wavelength: c = λf, where c is the speed of light, λ is the wavelength, and f is the frequency. This means that Δf = c/Δλ, and Δλ = c/Δf. Substituting these into the equations above, we get:

F(Δf) = ΔE / ΔtΔfΔA = ΔE / Δt(c/Δλ)ΔA = (ΔE / ΔtΔλΔA) * (1/c) = F(Δλ) * (1/c)

F(Δλ) = ΔE / ΔtΔλΔA = ΔE / Δt(c/Δf)ΔA = (ΔE / ΔtΔfΔA) * c = F(Δf) * c

So, to convert