Mirrored Cube

Factual Questions
1

Woke up this morning thinking about this…

First the setup:

You have a cube that where each side is say 1 foot square.
Inside of this cube is mirrored.

Suspended inside this cube is another cube 6 inches per side.
Outside of this cube is mirrored.

Each flat side of the smaller cube is facing a corner of the larger cube.

Now the Question:
How many Reflections would there be?

2

Answer will either be 12 or infinite depending on your definition of a reflection.

If a surface is only capable of producing 1 reflection by definition, then you have 12 surfaces to reflect off of.

If your talking about reflected images, then they would reflect back and forth multiple times, getting smaller each time, infinately.

3

There are two possible answers to this question.
[ol]
[li]An infinite number of reflections, since each reflection would in turn be mirrored over and over again.[/li][li]No reflections, since there is no light inside the box.[/li][/ol]

4

Six flat sides facing eight corners?

5

How “efficient” is an average mirror? They must absorb some energy, and if so the reflections wouldn’t be infinite.

I have a related question. Suppose a person were placed into a room with perfectly mirrored internal walls. He turns on a bright light and then turns it off. Would the room “dim” as he absorbs the light? Any ideas how long this might take?

6

If the mirrors are flat, then the images are all the same size. They’re further away, but they don’t shrink any more than I do when I walk away from you.

And dlack, the short answer is “very, very quickly”.

7

Aluminum is about 90% reflective. Household mirrors have the back surface coated, so I’d guess the front surface reflects between 5% and 10%, and the aluminum surface reflects about 90% of the remaining light. (Yes, all household mirrors produce double images.)

With multilayer coatings, it’s possible to make mirrors with reflectivity of 99% or higher.

If the room is 3 meters long, light hits the mirror every 10 nanoseconds. If the mirrors are 90% reflective, it takes only 100 nanoseconds before 2/3 of the light is absorbed by the mirrors. In just 1 microsecond, 99.997% of the light is gone.