If there was a sphere...

Question

And on the inside of the sphere the walls were entirely mirrors, what would the reflection be of?

Answer 1

Woah that's an awsome question....

but i'm not to sure it would reflect anything due to a lack of lighting...

Answer 2

More information is needed.

You need sources, and sinks, of photons.  Then it's easy to trace their trajectories inside your sphere.

Answer 3

The centre.

Wait.. revising that...

I don't really know? Depends on where you are. If you were at the centre, then the entire room would look like your head.

Answer 4

Assuming that the inside of the sphere is a very smooth spherical mirror (as opposed to a collection of flat mirrors stuck next to each other).

Assuming that you have a light source somewhere in there.

Assuming that you are looking from a given point inside the sphere.

Then you could reduce the problem to a disk that contains the centre of the sphere, your eye and the light source.  (with three points in a 3-dimension space, you can always define a plane).

It should then be possible to draw a line through your eye and the centre.  This will be a diameter.

You should also be able to draw another diameter through the centre and the light source.

The general case assumes that neither the light source nor the eye are located exactly on the circumference (i.e., exactly at the mirror surface).

Then, there will be exactly two points where the light from the source is reflected directly to the eye with only one bounce.  This is found by drawing the diameter that bisects the smaller angle formed by the two diameters.

A bit more complicated, you can find four points where the light is seen after two reflections,  nine with three reflections.

You can show that the entire circumference shows an image of the light source.

From the eye, there will be a band of reflection, along the projection (onto the sphere) of the plane that contains the three points: centre, eye, light source.