# Between two mirrors. Real experiment.

1. May 31, 2004

### Michael F. Dmitriyev

I would like to offer one simple experiment. It can be repeated by everyone. I am interested in conclusions which it is possible to make of this experiment. In my opinion, a correct conclusions can have the important consequences.
So.
Two flat mirrors are located in parallel on distance 1 meter (this distance is not critical). Between them approximately in the middle some object is located. Better if it is a light source .
The point of observation, where your head is located also between mirrors, but is higher than object..
Now, we look at the mirrors.
The result of observation:
An infinite line of images of this object in both mirrors. This line of images has prospect.
Why?

2. May 31, 2004

### Integral

Staff Emeritus
There is not really an infinite number of images, it does fade out due to loses at each reflection. The many images are due to repeated reflections, thus each successive image further away by the distance separating the mirrors. As with your common experience things further away appear smaller. Thus the perspective of the image.

3. May 31, 2004

### Chen

I'm more interested in this experiment: A perfect sphere is made completely of reflective material (i.e a mirror), and you turn on a light bulb at the center of the sphere. What would it look like for someone standing inside the sphere? How would the sphere react to the ligh, would it get increasingly hot or something?

4. May 31, 2004

### Michael F. Dmitriyev

If to draw optical lines between object and FLAT mirrors, then it will not be any visible repeating images. They should not be … But they are.

5. May 31, 2004

### krab

Poof

The light would burn out in short order because its own light is focused back onto itself. The sphere itself if perfectly reflective, would stay cool. The observer would just see a light go poof right after turn-on.

6. May 31, 2004

### Chen

Let us draw a line that is perpendicular to both mirrors and goes through the object itself. If you were watching either mirror from any point on that line, you would indeed only see one image on either side (I'm pretty confident of this). But since this is not physically possible (because you will either get in the way of the object or the object will get in your way), you must be a bit higher than the line, and that's when you start seeing multiple images. You will notice that the higher you are above that line, the greater the vertical distance is between the multiple images in each mirror. And as you approach the line, the distance approaches zero.

7. May 31, 2004

### Chen

I don't understand how light can "burn out" or "go poof"... can you please explain this in more detail?

8. May 31, 2004

### krab

Don't know what you mean. Draw a line from source to eye, reflecting once off the mirror, observing the law of reflection. That gives image 1. Now draw one that bounces off mirror 1, then off mirror 2, then off mirror 1 again, then into eye. That is image 2. Notice angle of ray from this second case is different from angle in first case, so observer sees 2 images at different locations. Continue to infinity with more and more bounces.

9. May 31, 2004

### krab

It gets too hot and melts. You have to realize that the power dumped (presumably electrically) into the light bulb has nowhere to go, since it cannot be absorbed by the sphere, which is perfectly reflecting. so the energy effectively stays in the light bulb. You can easily do this experiment. Take a 100 watt bulb, and wrap tin foil tightly around it. Or,.. don't try it. You could start a fire in the socket.

10. May 31, 2004

### Chen

Neat... I think I'll try this little experiment tomorrow (but outside the house and with a battery). If I don't come back tomorrow, be sure not to try this yourself.

11. May 31, 2004

### Michael F. Dmitriyev

In this case the energy inside sphere will collect and events will develop on one of scripts:
1) the light source will be broken;
2) in consequence of growing thermal movement, the sphere will lose the spherical form and will be destroyed in a result.

12. May 31, 2004

### Alkatran

Is it possible to have a sphere of material that lets light in, but not out? (The sphere would have more and more light, until the point where it absorbed it as quickly as it entered.. how hot would it be...)

I almost said "the sphere would get brighter and brighter", but caught myself

13. May 31, 2004

### Chen

Depends on your definition of "letting light in". If you place a battery-operated light bulb inside such a sphere, then you're basically just emitting photons into its space. You could call that letting light in, but then maybe not - because the energy already exists inside the sphere in the form of the battery.

14. May 31, 2004

### Michael F. Dmitriyev

I do not think, that this is correct explanation.
Let's simplify a problem.
Let there will be one flat mirror and one object.
Do you agree, what the image will be observed on distance 2r from object?
Here r – the distance between a mirror and object.

15. May 31, 2004

### Chen

I don't know about krab, but I agree.

16. May 31, 2004

### krab

Yes. 2r is distance of object from image.

17. Jun 1, 2004

### Michael F. Dmitriyev

Then you should agree, guys, the image will be not on a surface of mirror but behind it on a distance r. Though, if we draw an optical lines, they will not leave a surface of mirror and the image should be on distance r from object. Hence, this way of reception of the image is not relevant for a flat mirror.
Let’s assume the position of object in the space as {x, y, z}
To the mirror image of object concerning a plane of mirror the position {-x, y, z} corresponds.
x=r in our case.
We note, dimension x is perpendicularly , but y and z both are parallel to a plane of mirror.
Why the mirror changes a sign on one dimension (x) only and does not do it for y and z?

18. Jun 1, 2004

### Chen

Because the mirror lies exactly on the YZ plane, so it only has effect in the X axis. If you were to tilt the mirror, or change the axes, you would notice it also changes the Y and Z coordinates of the image.

19. Jun 1, 2004

### krab

Say origin is midway between mirrors, observer at x, object at x_o, mirror separation is 2d. THen in your notation, x_o+r=d. Distance in x-direction object to observer is x_o-x. x-component of vector of observer to images are as follows:
2d-x_o-x=2r+x_o-x
2d+x_o+x=2r+3x_o+x
4d-x_o+x=4r+3x_o+x
4d+x_o-x=4r+5x_o-x
6d-x_o-x=6r+5x_o-x
6d+x_o+x=6r+7x_o+x
8d-x_o+x=8r+7x_o+x
8d+x_o-x=8r+9x_o-x
etc...
Many times I've done these kind of calculations to find the effect of parallel-plate boundaries on the electric field of a charge distribution. It's the same problem, and there is no mystery.

20. Jun 1, 2004

### Olias

You are correct, I was thinking about the original poster, and gave the wrong link

Actually if you could remove/edit your post so that the 'link' is removed I would be grateful, thanks again.

Last edited: Jun 1, 2004