# Why do we need to define both luminous intensity and illuminance?

### Background

If a source radiates $\newcommand{\e}{\mathrm e} \Phi_\e$ total energetic flux (in watts $\rm W$), then it is said to radiate luminous flux $\newcommand{\v}{\mathrm v} \Phi_\v$ defined by

$$\Phi_\v = K_{\rm cd} \int_{0\ \rm m}^\infty V(\lambda) \, {\partial\Phi_\e \over \partial\lambda} \, d\lambda$$

where

• $K_{\rm cd} = 683\ \rm lm/W$ is the defining constant associated with photometric units;
• $V(\lambda)$ is the luminosity function, a dimensionless weighting function scaled to unity at maximum that represents relatively how sensitive the average human eye is to any particular wavelength of electromagnetic radiation; and
• $\lambda$ is the wavelength of the radiation.

### What I understand

Luminous flux $\Phi_\v$ can be thought of as a measure of the ‘amount’ of a light a source emits. In addition, there are two important photometric quantities in terms of luminous flux:

• Luminous intensity $I_{\v,\Omega}$, measured in $\rm lm/sr=cd$, represents the amount of luminous flux radiated through space per unit solid angle (where of course the solid angle is subtended with respect to the location of the source of radiation).
• Illuminance $E_\v$, measured in $\rm lm/m^2 = lx$, represents the amount of luminous flux incident on a surface.

### Question

Why are both of these quantities of interest in photometry? It seems to me that they both measure ‘brightness,’ which decreases as the distance from a light source increases. If you could provide an answer with an example of how both might be necessary to understand a situation or with an explanation of how they are distinct with reference to human perception, I would appreciate that.