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 The Shadow in a Sphere (Posted on 2009-08-19)
Consider a hollow sphere of radius R, in which a light source is placed at its centre. A square plate of side length S is held in place within the sphere by a pole of length L units. The square plate's position is then such that the displacement between the centre of the square and the light source is R-L units.

The square plate is also oriented in a way such that an imaginary line drawn perpendicular to the surface of the plate and passing through the plate's centre will pass through the light source.

Determine the surface area of the shadow formed on the spherical shell, due to the square plate.

 No Solution Yet Submitted by Chris, PhD Rating: 4.0000 (4 votes)

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 re: clarification | Comment 2 of 7 |
(In reply to clarification by Daniel)

I'm assuming there are no reflections to consider, especially as any ray from the center would be reflected back to the center if that were the case, so it would be back in the no-reflection mode anyway.

Because the author states that the distance from the center of the sphere to the center of the square is R-L, the end of the pole that's not attached to the square must be attached to the surface of the sphere, in the center of the shadow.

By coincidence, just a couple of weeks ago I had installed in my house a lighting fixture in the form of a sphere, with a bulb at the center (no square making a shadow, though).

 Posted by Charlie on 2009-08-19 12:45:49

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