Here’s an interesting question—at what distance can the human eye detect a candle flame?
Put this conundrum to Google and the first answer says it is possible to see a candle flickering up to 48 kilometers (30 miles) away, considerably further than the horizon. Can that be true?
Today, Kevin Krisciunas and Don Carona at Texas A&M University in College Station put this question to the test. And the answer is considerably less than the web would have us believe.
The big problem with testing this idea is the distance involved. For an observer on the ground, the Earth’s surface curves away at a distance of about five kilometers so a candle further than this would be below the horizon. Then there is the problem of obstructions such as trees and buildings and of other light sources that might fool the eye or change its receptiveness.
So Krisciunas and Carona looked for a way round this and, as astronomers, soon found one in the way humans view stars.
The brightest stars, such as Vega, have a magnitude 0. At what distance would a candle flame be comparable to a star like Vega, they asked.
Some straightforward nighttime experiments with a candle suggested that the distance was 338 meters. “To our eyes the candle flame and Vega appeared of comparable brightness,” they say.
To check, the team observed both Vega and the candle flame using the same digital camera (an astronomical SBIG camera with 35mm aperture and 100mm focal length).
The results were something of a surprise. “The candle flame at 338 m was 2.423 magnitudes brighter than Vega, even though they looked comparable in brightness to our eyes,” say Krisciunas and Carona.
That raises the question of how far away the flame should be to appear the same brightness as Vega. That’s not a straightforward question to answer because the camera’s CCD is sensitive to photons in a different way to human eyes and Vega and the candle emit light with different spectra.
Nevertheless, Krisciunas and Carona make some calibrating assumptions and say that parity would occur at 392 meters. In other words, a candle flame is the same brightness as a magnitude 0 star at a distance of 392 meters.
The faintest stars humans can see unaided have a magnitude 6. Fainter stars can only be seen using a telescope or binoculars.
Magnitude 0 stars are 251.2 times brighter than magnitude 6 stars. So while again taking into account the differences between starlight and candle light, it is possible to work out how far away the candle should be to appear equally bright as a magnitude 6 star.
Krisciunas and Carona say this would occur at a distance of 2,576 meters or roughly 1.6 miles, and that at 10 miles a candle would appear as bright as a magnitude 9.98 star. “This is far beyond the capabilities of the most sensitive human eyes,” they say.
So there we have it—the farthest distance a human eye can detect a candle flame is 2.76 kilometers.
That’s interesting work that adds to the debate on this topic. But it is unlikely to settle the discussions, particularly given that other work suggests the human eye can see flashes consisting of just a handful of photons.
What we need now is the definitive experiment that actually measures the issue in question—the maximum distance at which a human or group of humans can see a candle (as opposed to calculating the distance based on other measurements, as this work does).
That could be an interesting project for anyone with a few candles and a lot of time to spare.
Ref: http://arxiv.org/abs/1507.06270 : At What Distance Can the Human Eye Detect a Candle Flame?