Caption: The normalized blackbody spectrum equivalent of solar spectrum shown in 3 representations: wavelength, logarithmic frequency/wavelength (log fw representation) (AKA fractional bandwidth, and frequency. The blackbody spectrum equivalent is the spectrum the Sun were a perfect blackbody radiator with a temperature exactly equal to the Sun's actual effective temperature (a characteristic photospheric temperature) which this plot sets to 5775 K slightly different from solar photosphere effective temperature = 5772 K (current best value).

Features:

1. Obviously, the spectrum depends on the representation. So saying the solar spectrum peaks in the visible band (fiducial range 0.400--0.700 μm = 400--700 nm) requires specifying the wavelength representation.

2. The 3 representations in the plot give peaks at, respectively 502 nm = 0.502 μm (green band (fiducial range 0.495--0.570 μm), 635 nm = 0.635 μm (red (fiducial range 0.620--0.740 μm)), and 883 nm = 0.883 μm near-infrared (NIR, fiducial range 0.750--1.4 μm).

3. The energy distribution can be specified percentiles for the a href="http://en.wikipedia.org/wiki/Wavelength">wavelength representation: 10 % (< 0.380 μm), 25 % (< 0.502 μm), 50 % (< 0.711 μm), 75 % (< 1.065 μm), 90 % (< 1.624 μm), 90 % (< 1.624 μm), 100 % (< ∞).

4. We suggest that the logarithmic frequency/wavelength (log fw representation) is the natural representation for all spectra.

   The argument:

   1. The differential relationship among the representations (omitting unnecessary constants) is

        
        dE = I_ν dν = νI_ν(dν/ν) = -λI_λ(dλ/λ) =  -I_λ dλ  ,

      where ν is frequency, I_ν is the representation, λ is wavelength, I_ν is the wavelength representation, the minus sign is because increasing frequency dν causes decreasing wavelength dλ, and νI_ν = λI_λ

   2. Why do we have νI_ν = λI_λ? This is because we have the differential relationship:

        
        d㏑(ν) = dν/ν = - dλ/λ = -d㏑(λ)  ,  

      where the natural logarithm function is ㏑ and the relationship follows by taking the differential of the natural logarithm of the phase velocity relation νλ=c:

        
        d㏑(c) = 0 = d[㏑(νλ)] = d[ ㏑(ν) + ㏑(λ) ]
            = d㏑(ν) + d㏑(λ)    

      d㏑(ν) = - d㏑(λ) .

   3. Since νI_ν = λI_λ, there is NO difference which you evaluate and plots in the frequency representation and wavelength representation are identical, except for mirror reflection about the endpoints. This is a convenience.

   4. But more important the size in physical structures in frequency and wavelength tend to be proportional to their characteristic absolute size. For example, Doppler shift and cosmological redshift both shift frequency/wavelength by common factors C for all frequency/wavelength Thus, the logarithmic size of the shift is

        
       ㏑(ν_shifted/ν) = ㏑(C) = -㏑(Λ_shifted/Λ)  

      throughout the spectrum.

      The from the example and other cases is that log fw representation tends to give physical structures of equal importance relative their band equal importance in plots. This seems to yours truly a great boon.

   5. For blackbody spectrum the boon is also present. In the log fw representation, blackbody spectrum specific intensity (i.e., Planck's law) is

                                               x**4
        νB_ν(T) = λB_λ(T) = 2c[(kT/(hc)]**4 ---------- ,
                                            [exp(x)-1]   

      where the Planck constant h = 6.62607015*10**(-34) J·s (exactly), the vacuum light speed c = 2.99792458*10**8 m/s (exactly) ≅ 3*10**8 m/s = 3*10**5 km/s ≅ 1 ft/ns, and the x = hν/(kT) =hc/(kTλ) is dimensionless (i.e., unitless) variable incorporating frequency and wavelength information, where the Boltzmann contant k = 1.380649*10**(-23) J/K (exactly) and T is temperature. For reference for the fundamental physical constants, see also NIST: Fundamental Physical Constants.