Are I(nu, T) and I(lamda, T) Equivalent in Planck's Law?

[nicktacik]

On the wikipeida page http://en.wikipedia.org/wiki/Planck's_law_of_black_body_radiation

two formula's are given for spectral radiance, I(nu, T) and I(lamda,T). However, I(nu, T) seems to have units of J/m^2 and I(lamda, T) seems to have units of J/s/m^3. My homework question is to show that these expression are equivalent, however the fact that the units don't work boggles my mind. Does each expression represent something different? Can someone please shed some light on this?

 

[lalbatros]

Remember the definitions.
Remember that for example I(nu,T) gives a density with respect to the frequency scale. The units you have indicated could be seen in another light: W/m²/Hz. I like the "/Hz" units! It is convenient to think that: I(nu,T)*d(nu)*Surface is a power.

Observe that using the same notations for I(nu, T) and I(lamda,T) is not really a good idea because these are different functions, but it is common practice.

 

[nicktacik]

Oh, so I(nu, T) is really I per unit frequency and I(lamda, T) is really I per unit wavelength?