The difference between the lux and the lumen is that the lux takes into account the area over which the
luminous flux
is spread. 1000 lumens, concentrated into an area of one square metre, lights up that square metre with an
illuminance
of 1000 lux. The same 1000 lumens, spread out over ten square metres, produces a dimmer
illuminance
of only 100 lux.
The measured intensity of a
light source
decreases along any line from the source. It falls in inverse proportion to the square of the relative distance traversed.