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.

 

[member 553083]

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!