If, theoretically, you were in an infinite sized room, and there was complete darkness. If you lit a candle, how far away would you have to be from this candle before you couldn't see it?

You're basically asking what the limits of human vision are. And you're in luck, there was a paper published this summer answering that question (summary here). The tl;dr of the paper is that the human eye can detect a single photon. If it happens to be one of the 10% of photons that enter your eye and actually trigger a rod cell.

“The most amazing thing is that it’s not like seeing light. It’s almost a feeling, at the threshold of imagination,” says Alipasha Vaziri, a physicist at the Rockefeller University in New York City, who led the work and tried out the experience himself.

So to actually answer your question. WA claims that a candle outputs 13 lumens of light. Which is about 1016 photons per second.

If you want to "see" 1 photon per second, then if my math is right (assuming your pupil has a radius of 4mm), you could go up to 300 km away and still get that one photon per second entering your eye.

EDIT: People below have brought up some interesting points. 1 photon/sec isn't really "seeing" it constantly. Humans seem to have a 'frame rate' of ~100 fps, so say we want to see 1 photon per 'frame', and assume that only 10% of the photons entering our eye hit the rod and trigger this photon perception.

Then, to constantly be registering ~1 photon in your eye from the candle the answer shifts to a distance of 9 km(5.5 miles). Which is still crazy far away for a single candle.

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