Decades ago, it was generally believed that no solid could be transparent to light for more than a few meters. Today it's known that non-transparency in transparent is due to a small handful of causes, including crystal boundaries and microscopic inclusions of opaque material. Today we've learned that extremely pure amorphous glass fibers can be transparent for tens or even hundreds of kilometers. That raises the question of what the moon would look like if it were perfectly transparent. Assume it's the same size it is now, in the same orbit, and is perfectly spherical. Assume it's immune to micrometeoroids, tidal stress, and radiation damage. Spheres don't make very good lenses, but that's only because they typically have a constant refractive index. If the refractive index varies smoothly with the distance from the center, it could have a perfectly sharp focus. How would the refractive index have to vary with depth for the moon to have a focal length equal to the distance to Earth's surface? (Is it practical to make (small) lenses on this principle today? If not, why not?) If the problem is underspecified, I'll further specify that the refractive index at the moon's surface should be 1, the same as the surrounding vacuum. That will prevent the surface from being reflective, since it's sudden changes in the refractive index that cause reflections. This would revolutionize astronomy, since it would turn the Earth- moon system into a giant telescope. You'd need to take very brief photos due to the speed of Earth's rotation. Either than or take photos (or naked eye observations) from a very fast jet that compensates for both Earth's and the moon's motions. If your first thought is that is that the moon would be a burning glass, leaving a trail of destruction during every solar eclipse, think again. In a week I will explain why that wouldn't happen unless someone beats me to it, which I hope they will.
On Tue, Mar 19, 2019 at 8:28 PM 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...
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. -- Gene On Tuesday, March 19, 2019, 8:28:44 PM PDT, Keith F. Lynch <kfl@KeithLynch.net> wrote: Decades ago, it was generally believed that no solid could be transparent to light for more than a few meters. Today it's known that non-transparency in transparent is due to a small handful of causes, including crystal boundaries and microscopic inclusions of opaque material. Today we've learned that extremely pure amorphous glass fibers can be transparent for tens or even hundreds of kilometers. That raises the question of what the moon would look like if it were perfectly transparent. Assume it's the same size it is now, in the same orbit, and is perfectly spherical. Assume it's immune to micrometeoroids, tidal stress, and radiation damage. Spheres don't make very good lenses, but that's only because they typically have a constant refractive index. If the refractive index varies smoothly with the distance from the center, it could have a perfectly sharp focus. How would the refractive index have to vary with depth for the moon to have a focal length equal to the distance to Earth's surface? (Is it practical to make (small) lenses on this principle today? If not, why not?) If the problem is underspecified, I'll further specify that the refractive index at the moon's surface should be 1, the same as the surrounding vacuum. That will prevent the surface from being reflective, since it's sudden changes in the refractive index that cause reflections. This would revolutionize astronomy, since it would turn the Earth- moon system into a giant telescope. You'd need to take very brief photos due to the speed of Earth's rotation. Either than or take photos (or naked eye observations) from a very fast jet that compensates for both Earth's and the moon's motions. If your first thought is that is that the moon would be a burning glass, leaving a trail of destruction during every solar eclipse, think again. In a week I will explain why that wouldn't happen unless someone beats me to it, which I hope they will.
It looks like math-fun mangled the formula. The index of refraction is sqrt(2-(r/R)^2). -- Gene On Wednesday, March 20, 2019, 9:19:25 AM PDT, Eugene Salamin via math-fun <math-fun@mailman.xmission.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. -- Gene On Tuesday, March 19, 2019, 8:28:44 PM PDT, Keith F. Lynch <kfl@KeithLynch.net> wrote: Decades ago, it was generally believed that no solid could be transparent to light for more than a few meters. Today it's known that non-transparency in transparent is due to a small handful of causes, including crystal boundaries and microscopic inclusions of opaque material. Today we've learned that extremely pure amorphous glass fibers can be transparent for tens or even hundreds of kilometers. That raises the question of what the moon would look like if it were perfectly transparent. Assume it's the same size it is now, in the same orbit, and is perfectly spherical. Assume it's immune to micrometeoroids, tidal stress, and radiation damage. Spheres don't make very good lenses, but that's only because they typically have a constant refractive index. If the refractive index varies smoothly with the distance from the center, it could have a perfectly sharp focus. How would the refractive index have to vary with depth for the moon to have a focal length equal to the distance to Earth's surface? (Is it practical to make (small) lenses on this principle today? If not, why not?) If the problem is underspecified, I'll further specify that the refractive index at the moon's surface should be 1, the same as the surrounding vacuum. That will prevent the surface from being reflective, since it's sudden changes in the refractive index that cause reflections. This would revolutionize astronomy, since it would turn the Earth- moon system into a giant telescope. You'd need to take very brief photos due to the speed of Earth's rotation. Either than or take photos (or naked eye observations) from a very fast jet that compensates for both Earth's and the moon's motions. If your first thought is that is that the moon would be a burning glass, leaving a trail of destruction during every solar eclipse, think again. In a week I will explain why that wouldn't happen unless someone beats me to it, which I hope they will.
Hi Keith: 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 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. 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. At 08:28 PM 3/19/2019, Keith F. Lynch wrote:
Decades ago, it was generally believed that no solid could be transparent to light for more than a few meters. Today it's known that non-transparency in transparent is due to a small handful of causes, including crystal boundaries and microscopic inclusions of opaque material. Today we've learned that extremely pure amorphous glass fibers can be transparent for tens or even hundreds of kilometers.
That raises the question of what the moon would look like if it were perfectly transparent. Assume it's the same size it is now, in the same orbit, and is perfectly spherical. Assume it's immune to micrometeoroids, tidal stress, and radiation damage.
Spheres don't make very good lenses, but that's only because they typically have a constant refractive index. If the refractive index varies smoothly with the distance from the center, it could have a perfectly sharp focus. How would the refractive index have to vary with depth for the moon to have a focal length equal to the distance to Earth's surface? (Is it practical to make (small) lenses on this principle today? If not, why not?)
If the problem is underspecified, I'll further specify that the refractive index at the moon's surface should be 1, the same as the surrounding vacuum. That will prevent the surface from being reflective, since it's sudden changes in the refractive index that cause reflections.
This would revolutionize astronomy, since it would turn the Earth- moon system into a giant telescope. You'd need to take very brief photos due to the speed of Earth's rotation. Either than or take photos (or naked eye observations) from a very fast jet that compensates for both Earth's and the moon's motions.
If your first thought is that is that the moon would be a burning glass, leaving a trail of destruction during every solar eclipse, think again. In a week I will explain why that wouldn't happen unless someone beats me to it, which I hope they will.
participants (5)
-
Eugene Salamin -
Henry Baker -
Keith F. Lynch -
Marc LeBrun -
Tom Duff