# How many optical photons are in a room?

Got interested in the question and came up with ~1 trillion particles. Would like to take some time of anyone interested to review my approach to the problem and help with side questions I got confused with.

Here is my take. My room is few meters long with ~15W light source. Assuming its COP is nearly 100% and average photon is 500nm (close to green but rounded up for simplicity), it is trivial to find a number of photons emitted per second.

The next part of the problem is to decide the lifetime of photons and here is what I get confused with. My way of thinking is based on a red laser pointer experiment: one can see a light spot right on a wall where it is directed to, but it does not get reflected good enough to see it on the opposite wall, hence most of the photons get absorbed on a wall, while some other portion gets reflected (otherwise nothing could be seen by eyes) and absorbed on the next obstacle. This way I derive that photon travels a room length once or two times. Taking it as 10m length I derive photon's lifetime.

That is all I did to come up with ~1*10^12 estimation.

1. Anyone knows, does it look like somehow close to the reality?
2. I've started with 15W of light energy, it seems quite a lot to me. If it all gets absorbed on a surface of my interior, I'd expect to notice some heating up, but it does not actually happen.
3. Taking power of a light source as a starting point does not look quite trusty to me. It requires me to know a few technical details about the source. Is there anything better to start estimation with?
4. If I want to go with wider picture and count all photons (not only visible ones) in a room, is it correct to assume there are only the following sources to add up:
• GPS, WiFi, cellular
• thermal emittance and sun light
• If you want, you can turn your light off and consider the dimensions of your room as a box at some temperature. Then the photons in the room will come from blackbody radiation. So the number of photons will depend on the size of the room but also the temperature of the room. en.m.wikipedia.org/wiki/… Commented Oct 20, 2022 at 14:53
• Thermal photons are by far the dominating source. If you use the formula which @UVphoton linked to (en.m.wikipedia.org/wiki/…), you find $10^{16}$ thermal photons in a room of $100\,$m$^3$ at room-temperatures. Commented Oct 20, 2022 at 18:07
• The red laser test underestimates reflectivity. The laser beam is reflected off the wall diffusively, i.e. its light is scattered into all directions. This is why you can see the red dot after all! So the whole room becomes redder, instead of there being a reflected laser ray which would (not, see above) produce a dot on the next wall. A quick googling tells me that for a wall paint to be considered white it has to reflect at least 80% of the incoming (visible) light. Commented Oct 20, 2022 at 23:28

Welcome to the physics stack exchange!

Your estimate looks reasonable to me for an order of magnitude estimate including only visible light. Addressing your concerns:

1. Yes. I would expect your largest sources of error to be the crudeness of your estimate for the mean photon lifetime (light colored reflective rooms could result in much higher values etc.) and your simplification of the light spectrum to a single wavelength.
2. 15W is not very much heating power at room temperature spread over a whole room. Your body is emitting more than 100W of heating power right now as you read this!
3. You could instead start with the brightness of illumination in the room, but that would require a light meter, and would begin to feel a lot like simply measuring the quantity you are trying to estimate. I like your way better.
4. No, there are a lot of sources of photons, and your list is far from complete. One prosaic source of large numbers of photons is the 60 Hz EM interference caused by the wiring in the walls of the room. Not much energy, but you are counting photons, not energy. Also, numerous virtual photons are exchanged every time two molecules collide. There is a huge quantity of electromagnetic interaction going on around us, and any electromagnetic energy exchange relies on photons in some way. My examples do not complete your list, but I hope they give a flavor for how monumental a task counting low energy photons could be.

Keep asking questions, and enjoy the journey!