maybe if we looked at this a different way, it would help. everybody, put down your bongs and listen up.
our candle is a source of light. the amount of light the candle puts out is measured in lumens.
now, if we go 1 foot from the candle, that light is dispersed over an area. so we measure the intensity at 1 foot away (don't forget it's evenly dispersed) and say "ok, this brightness is what we will forever more call one lumen per square foot." that's the definition someone came up with way back when.
now we're measuring the light from a single candle spread over some area, which just happens to be 12.6 square feet, since we're 1 foot away. and we have, again by definition, 1 lumen over each of those square feet.
so what is the intensity of the candle?
gold stars to anybody who says 12.6 lumens!
so what going on is this: we are taking the intensity of the light put out by the candle (a point source with no area), and converting that to an equivalent amount of light spread over some area. and when we multiply the foot-candle readings by the 12.6 ft², we are going backwards and figuring what the intensity of the source (lamp) would be.
hope that helps
