Bob day2012-06-13 21:09:06

I’m pretty rusty in calculus, and I’ve been trying to

understand how to get from the frequency form

of Planck’s radiation law:

I(f) = (2*h*f^3/c^2)(1/exp(h*f/(k*T)) – 1)

to the wavelength form:

I(Lambda) = (2*h*c^2/Lambda^5)(1/exp(h*c/(Lambda*k*T)) – 1)

where f is frequency, Lambda is wavelength, and h, c, k and T are

all constants, and f = c/Lambda. It seems to be more than just

substituting c/Lambda for f. I vaguely remember a theorem that

covers the situation. Can anyone point me to the name of that

theorem and, hopefully, its derivation?

— Bob Day

The last danis2012-06-15 16:21:04

I think you mean

I(f) = (2*h*f^3/c^2)(1/(exp(h*f/(k*T)) – 1))

….and

I(Lambda) = (2*h*c^2/Lambda^5)(1/(exp(h*c/(Lambda*k*T)) – 1))

Recall that I(f)df and I(Lambda)dLambda are the energy fluxes and

df=(-c/Lambda^2)dLambda.

—

Clive Tooth

http://www.clivetooth.dk

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