Re: On a dark night, how far away can a person see a lit candle?

Joe Brouillette 
906593888.Ph
On a dark night, how far away can a person see a lit candle?

Joe,

Thanks for your question.  I was able to find a useful resource to help me 
answer your question in the archives of the Mad Scientist.

http://www.madsci.org/posts/archives/mar98/890104368.Ph.r.html

Adrian Poppa's answer is specific to red laser light, but we can make some 
adjustments to the facts and formulas that are presented to get a figure 
appropriate to candle light.

Summarizing the above reference,   the effective brightness of a light 
source has to do with how much power the source is giving off, (watts per 
centimeter squared), and also the wavelengthes that the source is giving 
off.  The human eye is most sensitive to green light, and the sensitivity 
falls off to only a few percent for red light.  For a light bulb, the 
effective brightness is only about a third of what would be expected from 
the power of the bulb.

I don't have any good data on candles, but I do know that their brightness 
is comparable to those small "nightlight" light bulbs.  These are usually 
rated at around 4 watts.  This means that the effective brightness of such 
a bulb, or a candle, is around 1 watt.

At a distance of 1 meter from the bulb/candle, the 1 watt of light power is 
spread over an area of about 12 meters square.  The power density is then 
about 8 * 10 ^ -2 watts per meter squared at a meter's distance.

In the referenced article, it is calculated that a minimum power density of 
6.28 times 10 ^ -15 watts per square centimeter is needed to see a red 
light source.  This is 6.28 * 10 ^ -11 watts per square meter.  Also, since 
the light of a candle is more efficiently detected by the eye than red 
light, this figure should go down.  If green light is 100% detected, and  
red light is 5% detected, then I estimate reddish yellow light to be about 
20% detected.  The minimum power density at the eye is then about 1.6 * 10 
-11 watts/meter squared.  

To get the maximum distance a candle is visible, I use a proportionality of 
the brightness of a candle at one meter to the minimum required brightness, 
keeping the inverse square relationship of distance to brightness in mind. 
 Dividing 8 * 10 -2 watts/meter squared by
        1.6 * 10 -11 watts/meter squared gives a 
ratio of  5 * 10 ^ 9.   The square root of this is about 7 * 10 ^ 4 or 
70,000.  This means that the distance where the brightness of the candle is 
at the minimum brightness visible to a human eye is 70,000 meters, or 70 
kilometers, or about 43 miles.  

This distance seems rather large, but keep in mind that this is a 
theoretical maximum distance.  You probably would have to use a trick known 
to amatuer astronomers called averted vision. This involves not looking 
directly at a light source, so that you are using the most light sensitive 
part of your retina, the rods, to detect the light source.

Also keep in mind that many approximations have been made in this 
calculation.  In the original article, Adrian Poppa notes that a 1 
milliwatt red laser is easily seen over a distance of 20 miles, even when 
the calulation predicts a maximum distance of only 3 miles.

It might be an interesting project to try to test this on a clear night 
with friends.  All you need are candles or other light sources, a clear 
line of sight over several miles, and a telephone to coordinate everyone's 
actions.

Best regards,

Everett Rubel