Can we see a single candle X miles away?

Question

Recently I saw a commercial for Centrum that claims you can see the light of a single candle from ten miles away.

I was skeptical, but a trip to the internet claims that not only is that true, but you could actually see it from 30 miles away. Most of what I found simply repeated that claim (some had varying numbers, but in the 10-30 range) with nothing to back it up. One page detailed it a bit better, by giving some basic math based on the number of photons it takes to register a light in the eye. However, they still don't link to anything solid IMO.

Obviously these numbers assume line-of-sight, since any distance over a few miles would be blocked by the horizon if on the Earth's surface. I also assume that "the light from a single candle" means roughly one candela, but nobody cares enough to clarify that I could find.

The main reason I'm skeptical is because I've seen ceremonial (small) bonfires on mountains a few miles away. Even with a much larger light and closer distance, they're pretty faint.

Is there any empirical evidence that human eyes can see a light source that small from that distance? This seems like a simple thing for people to test.

Answer 1

What you described sounds like the Absolute Threshold in neuroscience. It is commonly defined as "The lowest amount of stimulus that a person can detect 50 percent of the time."

According to an experimental research conducted by Hecht, Shlaer, and Pirenne (1942), the smallest number of photons that could elicit a visual experience is 90 photons, while physiologically, human eye can detect as few as 9 photons.

Now, I don't really know how that amount of photons translated to a candle from 30 miles away, but Gale Encyclopedia of Psychology (2001) did give an example of Absolute Threshold for human vision as follows:

The amount of light present if someone held up a single candle 30 mi (48 km) away from us, if our eyes were used to the dark. If a person in front of you held up a candle and began backing up at the rate of one foot (30 cm) per second, that person would have to back up for 44 hours before the flame became invisible.*

So, yes, there is an empirical evidence for it. But it is highly unlikely for it to happen in real-life experience, as there are many other factors that influence our perception of a stimulus, such as motivation, expectation, adaptation to the stimulus, cognitive process, not to mention many other stimulus that we perceive and process in real-life experience at any given time.

Answer 2

This page, which includes relevant calculations, suggests a limit closer to 10km.

The calculations compare seeing a candle to seeing a 6th magnitude star. There's additional discussion assuming an ability to see 7th and 8th magnitude stars, but 6th is generally considered the naked eye limit.

Even 10km strikes me as ambitious, since it does not take into account atmospheric seeing which would "smear" the candle into an extended object, lowering its "surface brightness" considerably. Additionally, while the page mentions light pollution, in most locations that would have a dominant effect (just as most nights, most of us cannot see 6th magnitude stars).