Firstly, let's define the following:
The color temperature of a light source is defined by comparing its color within the light spectrum with that of light that would emit a black body heated to a certain temperature.
In this sense, the Wien's law, relates the wavelength [tex]\lambda_{p}[/tex] where the intensity of the radiation is maximum (also called peak wavelength) with the temperature [tex]T[/tex] of the black body.
In other words:
There is an inverse relationship between the wavelength at which the emission peak of a blackbody occurs and its temperature.
Being this expresed as:
[tex]\lambda_{p}.T=C[/tex] (1)
Where:
[tex]T=3500K[/tex] is the temperature in Kelvin (K)
[tex]\lambda_{p}[/tex] is the wavelength of the emission peak in meters (m).
[tex]C[/tex] is the Wien constant, whose value is [tex]2,898(10)^{-3}m.K[/tex]
Then:
[tex]\lambda_{p}=\frac{C}{T}[/tex] (2)
[tex]\lambda_{p}=\frac{2,898(10)^{-3}m.K}{3500K}[/tex]
[tex]\lambda_{p}=0.000000828m=828nm[/tex] This wavelength corresponds to red color.
Therefore:
