Understanding the Rayleigh-Jeans Approximation: Where Does the Negative Sign Go?

[the riddick25]

i have a quick question, which hopefully someone can straighten out for me.

i was reading this http://en.wikipedia.org/wiki/Rayleigh-Jeans_law
at the part titled 'Consistency of frequency and wavelength dependent expressions'

i follow the logic, but am confused about where the - sign goes after the differentiation.
they differentiate, and get the negative, but when this is multiplied by the frequency dependent form, it disappears.
and i now know this cannot be a typo, because i have found other references which also have the answer as a positive.

could someone please explain where this negative goes, and for what reason.

thanks :)

 

[cepheid]

The negative sign arises because wavelength and frequency are inversely related, so that an increase in one quantity corresponds to a decrease in the other quantity. However, the total power (per unit solid angle per unit area) contained in the frequency interval bounded by ν₁ and ν₂ is the same regardless of whether you measure the change in frequency as "going from" ν₁ to ν₂ or as "going from" ν₂ to ν₁. In other words, the "change in" frequency (or wavelength) is not really relevant, only the width of the interval is. We don't care about the direction in which you integrate. I suppose they could have written

|B_νdν| = |B_λdλ|

or something like that, in order to make things explicitly clear.

 

[the riddick25]

Thank you!

I couldn't find anywhere which told me that, they either just had the final equation, or just did the step without explaining why.

thanks again :)