Why Do I Get W/nm Instead of W When Calculating Spectral Output?

[Umabel]

I'm told the spectral radiance of a source is in the following units

W
----------------
cm^2 * sr * nm

And I try to use this to figure the spectral output of monochromator (in W), but I can't seem to cancel out the units. I multiply the spectral radiance by four other terms

slit width (cm)
slit height (cm)
solid angle, using a quick "f-number" equation (sr)
and then the transmission optics factor, which I assume could be unitless but I could be wrong.

Anyways, anybody know why I get W/nm instead of W? Or is it really just W?

 

[big man]

What would be the wavelength of the transmitted light from the monochromator?

 

[Umabel]

I assume the source is monochromatic here, so the wavelength coming out of monochromator is also monochromatic...let's just say that the radiation is at 400nm or something...

 

[big man]

So...what happens when you multiply your original equation by the transmitted wavelength??

 

[Umabel]

If I multiply the rest of the equation by let's say, 400nm, then the nm units cancel out...

edit: though I have to admit that I am not totally convinced that this is what the unit implies. Is it some invisible reminder that the spectral radiance depends on what wavelength region this source is emitting from?