Q:

A light bulb emits a finite number of photons. Is there a limit to the number of observers that will be able to "see" the light bulb?

- Lea Fredette (age 48)

Hebron, ct

- Lea Fredette (age 48)

Hebron, ct

A:

Dear Lea,

First of all you have to express the light intensity as so many photons per second. Secondly you have to specify a time interval in which to ask the question such as: "In a time interval of one second how many photons will enter an eye?"

Let's make a crude estimate. A 100 Watt incandescent will produce about 5 Watts of visible light, the rest going into heat. The energy of a single photon is of the order of 2 - 2.5 eV (electron Volt) for a single visible photon. So the number of photons emitted per second is 5 Watts. Now if you turn on the bulb for 1 second the total number of photons is 5/e = where e=1.6 x 10^{-19} , about 3 x 10^{19}. That's a whole bunch and you couldn't get all the people in the same room together.

That's not the end though. In order to see a photon it has to enter the pupil of an eye. The radius of an average pupil is about 3 mm. Now the intensity of the light falls off as the distance squared so the probability of a photon entering the pupil is ~(3mm/L)^{2}. So if the observer is 1 kilometer away the probability of one photon entering the eye is (3x1^{-3}/10^{6} )^{2}/4 = 2.2x10^{-18}. For the one second flash an observer would get about 70 photons. That's probably enough to identify it if you know when and where to look.

These numbers are very crude and I may have made more than one mistake so take my answer with a grain of salt.

LeeH

p.s. You may also be wondering about a more abstract, "in principle" answer. There are processes by which single photons can be converted to pairs of less energetic photons in non-linear crystals. (The reverse process is used to make visible light from powerful infrared lasers.) So there's no rigid "one photon gives only one observation" rule. (That's not the only argument against that rule, but it's a simple one.) Mike W.

p.p.s. In fact, there are difficult experimental techniques that one can do to measure the presence of a photon without destroying it. These measurements are called QND (quantum non-demolition) measurements. David S.

*(published on 03/19/2014)*