Does a Webcam Record Infinity When Pointed at a Computer Screen?

[fromaage]

...and you can peer into infinity, right?

Now consider pointing a webcam into a computer screen showing its output image. Is the light source at the center of the image recorded by the webcam at infinity?

 

[Danger]

Welcome to PF, Fromaage.
Even with regular mirrors, as opposed to the camera setup, you will not get infinite images. There will always be losses, and that would be compounded by having electronics involved, since the efficiency would be lower.

 

[fromaage]

Let's assume we have a perfect mirror with no reflective losses and a webcam-monitor system with no losses also. What happens then?

 

[TVP45]

When I did this experiment, I got to maybe thirty or forty images (It's been decades, so I don't remember the exact number) before the image got too small to distinguish. Modern cameras are much better resolution, and you could always adjust the image to be just slightly smaller each time (if the image is exactly the same size, I think it's a meaningless experiment), but there is still some limit way before infinity.

When cameras had plumbicon tubes, you could do an interesting (if expensive) experiment by defeating the AGC/limiter circuits and cranking the brightness of the center toward infinity and you'd get the same nice burn as if you had pointed it at the sun. I don't think a modern device will allow anything like that, but it might be worth a shot if you've got a few bucks to spare.

 

[Archosaur]

Let's assume we have a perfect mirror with no reflective losses and a webcam-monitor system with no losses also. What happens then?

Okay, you have two perfect mirrors. In order for them to reflect off of each other indefinitely, they would have to be perfectly parallel. So let's say they are. The light is bouncing straight back and forth. But now what? How do you see the image? In order to see it, the light would have to enter your eye, but all the light is bouncing back and forth between the mirrors. I'm sure we've all noticed that, when you try to "see infinity", your head is in the way. One way to fix this could be with a one-way mirror.

Let's say we have perfect one-way mirror (one side is perfectly transparent, the other perfectly reflective. Obviously, this could not really exist) and perfect traditional mirror. We have them set up so they are perfectly parallel with each other, with the reflective side of the one-way mirror facing the other mirror. We then stand behind the one-way mirror and look through.

Do we see infinity?

Not quite. Here's why. We've all noticed the "layers" that appear when we do something like this. The closer to parallel the mirrors are, the more "layers" can be seen. Mathematically speaking, perfectly parallel mirrors would result in unlimited "layers".

But not really.

One "layer" is created, every time the light gets from one mirror to the other. It then bounces back to the first mirror, creating another "layer". Light travels at 299,792,458 m/s.
So, if our mirrors were 1 meter apart, that would mean that 299,792,458 "layers" would be added to the image every second.

So, you would see further and further at an inconceivable rate, but the image would never be "complete". You wouldn't "see infinity" no matter how long you waited.

The same thing can be applied to a webcam and a monitor, but on top the speed of light being a factor, the processing speed of the computer would determine the rate at which "layers" are added. It takes some time for the image the camera sees to show up on the monitor and go back into the camera. This is made obvious when you move a webcam from side to side. Depending on the computer, there may be considerable lag between the motion of the webcam and the image on the screen. I know that when I aim my webcam at my monitor, I can actually see the "layers" being added one at a time. Your computer may be fast enough that you don't notice, but no matter how fast it is, the "layers" are added one at a time. Even without any loss, you can't see infinity.

 

[elsabinoe]

Surely you could never "see infinity" because the molecular structure of the mirror itself would be too small at some point and the light would diminish over time/space?

But...would it be possible to measure a tiny difference in time (ie. 1/1000 second) if the two mirrors were 10m x 10m and they were spaced 10m apart. One mirror is (although theoretically and practically impossible) a perfect one-way mirror with a telescopic lens behind it.

How many repetitions/layers would the camera need to see down before it would be able to record a noticable difference between "layer time" and "real time"?

If real time and layer time could then be displayed simultaneously with, for example, a tennis ball inbetween the two mirrors, then one could demonstrate the relationship between light and time in, for example, a science museum setting.

I have wondered for several years if this is practically managable but have never been able to do the maths properly. Especially when you need to include the formula for the diminishing light. We can assume that the initial amount of light can be very high in terms of lumens and the photons could be prevented from escaping by having the mirrors inbetween some kind of tunnel.

 

[DaveC426913]

Let's say we have perfect one-way mirror (one side is perfectly transparent, the other perfectly reflective. Obviously, this could not really exist) and perfect traditional mirror. We have them set up so they are perfectly parallel with each other, with the reflective side of the one-way mirror facing the other mirror. We then stand behind the one-way mirror and look through.

Do we see infinity?

No, we see nothing (i.e. black). If one side of the mirror is perfectly reflective then no photons will pass through it to reach us.

This isn't just a limitation with "real" mirrors; it is the case even in an idealized thought experiment.

 

[Archosaur]

Hahaha! I must have grown a lot since I wrote that.

I was reading it, thinking "haha, look at this idiot. Dave's about to tear him a new... oh..."