Consider a sphere with radius R which is made by a mirror like material, so that it can reflect very well light. At a distance D from the center, we direct a narrow beamlight. If it is pointed towards the center , of course, it will be bounced back. We now adjust the beam of an angle theta so that it will we deflected vertically. Find theta function of R and D.

Question

anonymous · Answer

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anonymous · Answer

Hi, do you know what the answer's supposed to be ?
I used the sine law to get a trignometric equation for theta R and D but I would only be able to solve it graphically.
Maybe someone else can do better.

anonymous · Answer

Hi again, I think I might have the answer for your problem.
I found it easier to solve by including the impact parameter in the diagram.
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I'm not completely sure that my answer is correct but it predicts theta going to 0 as D goes to infinity, as expected, and it predicts theta = 25 degrees for the case that D=2R
I haven't got a protractor to check the second case carefully with a diagram.