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imagine standing inside a sphere composed entirely of mirror surface; what does this look like?

  1. inside is lit by an invisible light source

  2. if each point encounters a reflection of itself, what is reflected?

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    $\begingroup$ have you seen this? $\endgroup$ – john Jul 23 '15 at 7:47
  • $\begingroup$ @john thats pretty cool. Though, I think what I'd really like to know is what the inside looks like when it's empty. It's easy enough to explain the reflection dynamics when there is another object present to reflect, but what if the sphere is empty? $\endgroup$ – Benjamin James Jul 24 '15 at 23:36
  • $\begingroup$ If it's empty of any light, then it looks like an empty square room. $\endgroup$ – anderstood Jul 25 '15 at 14:43
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From the interior, a spherical mirror can be analyzed as a continuous assemblage of concave mirrors. If you were illuminated by an invisible light source, your image would be reflected from all points on the interior surface according to the mirror equation for concave spherical mirrors:

(1/object distance) + (1/image distance) = (1/focal length)

The distance is the distance to the surface of the mirrors. The focal length of the mirrors is half the radius of the curvature (half the radius of the sphere). The location of the image will depend on where you stand inside the sphere. There will be an image of yourself wherever you direct your gaze. All reflected rays from the continuous assemblage of concave mirrors will converge at one image location, which will depend on where you stand inside the sphere. Depending on where you direct your gaze, your image will shift to different locations.

The magnification of a concave spherical mirror is the ratio of image distance to object distance. The absolute value of the magnification is:

|Magnification| = image distance / object distance

Once again, the magnification of your image will depend on where you stand and where you direct your gaze.

Here's a link that explains the optics of a concave spherical mirror: http://hyperphysics.phy-astr.gsu.edu/hbase/geoopt/mireq.html.

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