Who cares about angels on the end of a pin? Let’s get real; how many photons are there on the end of a match?

There’s a lot of data out there to help us calculate this; one article says that the human eye can detect a candle in the dark at 30 miles. Isn’t that something? The same article says it takes at least 54 photons just for the human eye to register an event. So that match (or candle) has to get 54 photons into that fraction of your eye that actually receives and focuses the photons. But the whole eye doesn’t actually receive the photons; it’s just the black opening in the middle. The largest it ever gets is about 7 millimeters diameter, which is 38.5 square millimeters in area, or .385 square centimeters.

How many events can the human eye see in one second? If we’re looking at the match from 30 miles away, and it looks continuous, then we are receiving over 50 frames a second (though the human eye has been recorded as being able to discern and identify an image in 1/255^{th} of a second, we’ll be conservative). If the image were less than 50 times per second, we would detect a choppiness in the image; still, overlap in the match’s photon emissions could turn a choppy image into a smooth one. But lets assume we get a continuous 54 photons, all the time, at least 50 times a second; anything less would look like a flicker off.

Now we have everything we need to calculate how many photons are coming off the head of a match!

Just put an eyeball…or just the iris, the bit that receives the light, in every spot in a 30 mile radius, add up the total number of irises, multiply by the 50 times-per-second, times the 54 photons per eyeball, and we should have the number we need.

The sphere of irises is 4*pi*r-squared. Or 4*3.14*30*30 = 11,310 square miles, or 29,292 square kilometers. Or 29,292,000,000 square meters. Or 292,920,000,000,000 square centimeters. Since each dissected eyeball (just the iris, you see) only takes up .385 square centimeters, that’s about 760,000,000,000,000 irises stuffed carefully into the perimeter of the sphere to capture all the photons. Just as a point of interest, that’s about 50,000 times the number of human eyeballs on Earth. Guess we’ll be dissecting all the other animals, too. May as well start with fisheyes; they’re sort of gross to begin with.

Each of those eyes is gathering 54 photons at least 50 times a second, so we get to multiply the 760 million million by another 250-ish, giving us a grand total of about 190,000 million million photons off the head of a match every second. Or, just because I like a lot of zeros, 190,000,000,000,000,000 photons. Every second. From a freakin’ MATCH HEAD. We are awash in a photon bath.

Now, leave the darkness of night, and realize that when you walk outside, you are no longer looking at one tiny spot radiating onto 190 quadrillion eyes, now you have a hemisphere of 30 cubic miles of daylight radiating onto your eyeball. Well, okay, you can’t look at the hemisphere all at the same time. Your turn to do the math! How many photons are hitting your eye every second? Hint; it’s an absolute crapload of photons.