Use of the Sun's gravitational field to focus light has been proposed as a way of making a super-high resolution telescope. https://en.wikipedia.org/wiki/FOCAL_(spacecraft) Brent On 3/20/2019 9:07 PM, Keith F. Lynch wrote:
Tom Duff <td@pixar.com> wrote:
Keith F. Lynch <kfl@keithlynch.net> wrote:
it's sudden changes in the refractive index that cause reflections. I'd never thought about this before, but a quick Google suggests that it's not true. Graded-index media have gradual Fresnel reflection. Here's a paper that purports to explain the details: https://pdfs.semanticscholar.org/9f8f/e29d292732c8a7fb1aa82f0ce5df94822077.p... Thanks. My intuition was that as the distance over which the refractive index changed significantly became large compared to the wavelength of light, the reflectivity, while perhaps never reaching exactly zero, went down faster than linearly. And if I understand the formulas right, my intuition is correct. One abrupt transition of one part in a thousand has a reflection coefficient of 2.5E-7, but ten transitions of one part in ten thousand each have reflection coefficients of 2.5E-9 for a total reflection coefficient of 2.5E-8. So with more than a trillion transitions, each of less than one part in a trillion, the total reflections should be unmeasurably small.
I can make no sense of the paper's distinction between electric and magnetic polarization, given that light is always both, with the two always at right angles to each other.
Digression: The reason the first transatlantic telegraph cable (1858) worked so poorly is because its impedance varied widely, resulting in lots of internal reflections that smeared out the signals. That's also why no transatlantic *telephone* cable was attempted until 1956. Of course in those cases the relevant wavelengths are much longer than those of light.
Eugene Salamin <gene_salamin@yahoo.com> wrote:
The Luneburg lens is a ball of radius R whose index of refraction varies as ?2-(r/R)2.? A parallel beam of light is exactly focused, in the approximation of geometric optics, to a point on the surface opposite the direction of entry. Thanks, but I'm interested in the focal point being at the surface of *Earth*, not at the surface of the *moon*. An f110 lens. That requires a very low index of refraction, probably unrealistic for any known form of glass.
It looks like math-fun mangled the formula.? The index of refraction is sqrt(2-(r/R)^2). The digest option replaces all non-ASCII characters with question marks, which makes some posts completely incomprehensible. Others can be decoded with effort. For instance I deduced that a recent mention of "?wave" in another thread, the ? was supposed to be the micro symbol. It's all Greek to me.
Marc LeBrun <mlb@well.com> wrote:
I don't know, but it seems like a fun question for XKCD... Unfortunately, he stopped doing the what-ifs months ago.
Henry Baker <hbaker1@pipeline.com> wrote:
Even if the Moon were made of 100% silicon glass, it would still probably not have a uniform refractive index due to compression effects of gravity at different depths. On the other hand, these effects might be just what is needed to get proper focus. I was making several unrealistic assumptions. For instance that the glass moon is perfectly spherical and perfectly rigid, i.e. no tidal bulge or equatorial bulge.
I seem to recall that the human eye lens has different refractive indices at different depths, but I don't know the profile. You also have a very significant problem of different points of focus for different colors/wavelenths. Designing a "Glass moon" which corrected for this would be an interesting engineering exercise. I designed it by fiat -- I chose a hypothetical kind of glass in which the refractive index is the same at all wavelengths. Also, it had better be *extremely* transparent, since otherwise the small amount of light absorption in the interior would soon melt the whole thing down.
It's impressive how little chromatic aberration the human eye has. The only time I notice any is when looking at a purple Christmas light from a distance when it's dark out. At best it's either a red point embedded in a blue haze or vice versa.
BTW, even if your "Glass moon" weren't in proper focus, you could still utilize it for its large light-gathering power, and use a *corrective lens* on the camera at the Earth's surface to bring things into better focus. This corrective lens might also be able to have different corrections for different colors. I don't think that would work. But even without proper focus, the light gathering would certainly be useful. Astronomers can learn a lot about an object without resolving it.
Similarly with using gravitational lenses to gather gravitational waves. Too bad the sun's focal length as a gravitational lens is so long. It would have been convenient had it been about the distance to the Earth.
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