Can't fool the square root of two!


Apr 27, 2002
Aurora, Ontario, Canada
Can\'t fool the square root of two!

In a couple of threads I noticed some surprise about the relative lack of difference between 250 and 500 lumen lamp assemblies.

Well, the subject line here says it all <smile>.

So if you go from 250 to 500 lumens and keep the center beam candlepower the same, your circle of coverage diameter will go up approximately by a factor of 1.414 (square root of two).

So if you are covering a 10 foot diameter circle at 250 lumens, it will then cover a 14 foot diameter circle at 500 lumens with the same brightness.

On the other hand, if you keep the circle the same diameter, then you'll have the same brightness at (for example) 141 feet that you had at 100 feet.

To get the same brightness at 200 feet that you had at 100 feet with the same circle of coverage, the lumen output would have to go up 4x.

Anyway, I thought I'd throw this out so that expectations are brought in line with reality...I know mine never seem to be <smile>.

Of course you knew all this and it still doesn't keep us from hoping...




Re: Can\'t fool the square root of two!

You think light is difficult ? Look at air;
if a 28 mph wind is giving you 400 watts of wind turbine power, then it dies down to a 14 mph breeze, your left with only 50 watts of power coming in, one eigth the power at half the speed...but you knew this also....
;> )


Newly Enlightened
Dec 19, 2001
Los Angeles area
Re: Can\'t fool the square root of two!

Well put, Richard. And, on cameras, each doubling of the F-Stop number say, from f2.0 to f4.0 represents the amount of light being divided by two...twice. The in-between numbers (f2.8 in this example) are half the light of the smaller number and twice the light of the larger. Crystal clear, right?

Light is much like sound in its measurement, just the names are different. In sound, a 3db increase in sound takes twice the power, 6db takes four times the power. I saw on TV one of the car stereo contests where they were testing how loud each competitor could play a test tone. One guy got a reading of 170db!!!! Needless to say, no one was in the car! Some of the cars had four guys in the crew laying on the roof of the car to hold it on! Another guy reproduced his interior with 1/4" steel. If we could just turn all that energy into light!