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Just another perspective: Since the sphere is non-ergodic, your observation depends on your and the source locations inside the sphere. For ergodic shapes (ellipsoid, etc), you will see an evenly lit world.


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'The mirror is given a momentum twice that of the incoming photon. As a mirror is typically quit heavy, lets say one gram. Its kinetic energy due to momentum it received will be extremely small. However, the photon will actually change its energy by the same amount, thus its wavelength changes, but not much.


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Since the photon reflects, its momentum changes: $p_{ph}'=-p_{ph}$. But total momentum of the system is conserved: $p_m+p_{ph}=p_m'+p_{ph}'$. Thus, the mirror will change its momentum. But, if the mirror has large mass, then it'll get very small energy from the collision. For zero-mass particle (photon) falling onto the mirror with mass $m_2$, the energy of ...


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Try this experiment: take a small mirror (so you can look over the top of it) and put it vertically on a piece of paper. Looking in the mirror in one position, try drawing a dot behind the mirror where you "see" the spot. Because the mirror is small you should be able to see where your pen is pointing. Now shift where you stand (without moving mirror or ...


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Do you mean that the spot on the mirror where you see the image changes? That's not the location of the virtual image. The location of the virtual image is not on the mirror, it is behind the mirror, at the location the box would have if 1.) your mirror were clear transparent glass and 2.) the box were really behind the mirror instead of in front of it. ...


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Increasing the contrast on the projected object might help some, as well as changing the lens, but probably the best (easiest and cheapest) way to increase the contrast on the final image is to edit it after the fact, using some image/video manipulation software.


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You've probably heard of a curve called the parabola, and you probably interpret this as meaning it's a function something like $y = x^2$. However there is another way to define the parabola. If you draw a line (called the directrix) and then choose a point (called the focus) not on that line then the set of points that are an equal distance from the ...


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There is also optgeo, quite simple, but could be useful in your case, you can drag and drop lenses, mirrors, beamsplitters etc. It is free software: http://jeanmarie.biansan.free.fr/optgeo.html It is also in the ubuntu and debian repositorys.


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Can't be done, yet. But don't expect 3d printing to stand still, it's only recently been born, wait till it starts walking, and running! My hope was that there could be a vacuum process that was usable in just enough vacuum to form a perfect mirror shape over a perfect mirror mold of some kind, then start the vapor deposition on the cheap, lightweight ...


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The highest resolution 3d printers I know of are around 1600dpi, which is a resolution of about 15$\mu m$. Telescope mirrors have to be smooth to fractions of a wavelength of light, so the resolution of current printers is nowhere near good enough. Whether 3D printers could one day be good enough is a different question, but given that the improvement in ...



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