Alaskan
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The sensors in the retina can respond to a single photon. However, neural filters only allow a signal to pass to the brain to trigger a conscious response when at least about five to nine arrive within less than 100 ms. If we could consciously see single photons we would experience too much visual "noise" in very low light.
A standard candle at 31 miles is 0.0000000004 (4x10^-10) cp. I highly doubt the eye could pick that up, even under ideal conditions. A good point of comparison would be how bright that would be relative to a magnitude 6 star, which is about the dimmest star anyone with normal vision can see. The sun is -26.8 on the magnitude scale. 5 orders of magnitude is a factor of 100 in brightness, so a 6 magnitude star is about 10^-13 as bright as the sun. The sun is roughly 100,000 cp, so a magnitude 6 star is 10^-8 cp, or about 25 times as bright as the candle. In other words, the candle is probably not visible from 31 miles, although it would be barely visible at about 6 miles.
A standard candle at 31 miles is 0.0000000004 (4x10^-10) cp. I highly doubt the eye could pick that up, even under ideal conditions. A good point of comparison would be how bright that would be relative to a magnitude 6 star, which is about the dimmest star anyone with normal vision can see. The sun is -26.8 on the magnitude scale. 5 orders of magnitude is a factor of 100 in brightness, so a 6 magnitude star is about 10^-13 as bright as the sun. The sun is roughly 100,000 cp, so a magnitude 6 star is 10^-8 cp, or about 25 times as bright as the candle. In other words, the candle is probably not visible from 31 miles, although it would be barely visible at about 6 miles.