Radiometry gives us the objective measure of energy and power of light sources. However, human eye does not respond to all colors of visible light equally. Consequenctly, we perceive intensities differently than an objective instrument. For instance, experiments have shown that, during the day (i.e., photopic vision), the eye is most sensitive to the yellow-green (at around wavelength of \(555\,\text{nm}\)) light than to the red and blue lights of the spectrum. Therefore, yellow-green light will appears brighter to our eyes than either the red or the blue light of the same intensity. At night (i.e., scotopic vision) the sensitivity blue shifts with peak around \(505\,\text{nm}\) wavelength.
To take the difference between actual physical power emitted by a light source and as perceived by a human eye, it is necessary to weigh the actual power by the human eye response function, called spectral luminance efficiency or the \(V(\lambda)\) function, whose value is between 0 and 1 and varies with wavelength of the light. These weighted quenties are called photometric quantities to distinguish them from physical radiometric quantities.
If we kept the photometric units same as the radiometric units we will have the following relation between photometric power emitted \(F_{\text{photo},\lambda}\text{,}\) called luminous flux, and the radiometric cousin \(P_{\text{radio},\lambda}\) (the power) at some wavelength \(\lambda\text{.}\)
\begin{equation}
F_{\text{photo},\lambda}(\text{Units: W}) = V(\lambda)\times P_{\text{radio},\lambda}(\text{Units: W}).\tag{43.13}
\end{equation}
But we express photometric quantities in lumin (\(lm\)) and radiometric quantities in Watts (\(W\)). The conversion factor is chosen to be
\begin{equation*}
1\,\text{W} = 683\,\text{lm}.
\end{equation*}
Thus, we include the conversion factor when writing Eq.
(43.13).
\begin{equation}
F_{\text{photo},\lambda}(\text{Units: lm}) = V(\lambda)\times P_{\text{radio},\lambda}(\text{Units: W}) \times \frac{683\,\text{lm}}{1\,\text{W}}.\tag{43.14}
\end{equation}
Luminous flux gives total power in wavelength \(\lambda\) over the entire solid angle of \(4\,\pi\,\text{str}\text{.}\) The luminous flux per unit solid angle is called lumninous intensity. Let us denote it by \(I_{\text{photo},\lambda}\text{.}\)
\begin{equation*}
I_{\text{photo},\lambda} = \frac{F_{\text{photo},\lambda}}{4\,\pi}\,\frac{\text{lm}}{\text{str}}.
\end{equation*}
The unit \(\text{lm.str}^{-1}\) is called a candela (\(\text{Cd}\)), the base SI unit of luminous intensity. Or, multiply \(\text{lm.str}^{-1}\) by \(4\,\pi\ \text{str}\) and you get
\begin{equation*}
1.0\,\text{Cd} = 4\,\pi\,\text{lm}.
\end{equation*}
A typical wax candle has luminous intensity of about \(1\,\text{Cd}\text{.}\)
