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Suppose an Earth-sized (convex) perfect lens is placed between the sun and the Earth (with the center of the lens on the line between the center of the Earth and the center of the sun, and the lens perpendicular to this line), how will the image of the sun that's projected on Earth look like? Now I don't know that much of optics, but I do know that the image of the sun varies with the diameter of the lens (when I played with lenses to start a fire the image was very little). I know how to construct the image of an object, but in this case, the huge scale (the distance to the sun included) confuses me.

Because of the big diameter of the lens, and the big size of the sun, there will be a big image on the Earth (because of the curvature of the Earth the image is blurred; only circles on the Earth with a diameter varying from zero to the magnitude of the Earth's diameter can be in the focal plane). Because of the big distance (between the Earth and the sun) it's hard to draw an image. How varies the magnitude of the image on the surface of the Earth (which is blurred because the surface of the Earth is for the not in the focal plane of the lens) with the strength (and thus the focus and the distance of the lens to the Earth) of the lens and can the image of the sun projected on the surface of the Earth be smaller than the Earth's diameter so in some parts it looks like night and in the other parts the sun shines more intense?

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closed as unclear what you're asking by sammy gerbil, Jon Custer, Yashas, John Rennie, coconut Dec 13 '17 at 17:13

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The level of destruction for this scenario is... interesting. Depending on the eccentricity of the lens (that may be the wrong word, but whatever), this could vary from 'practically nothing' to 'WATCH ME BURN THE WORLD!!11!!1!!!!'.

Anyways, now that we're done maniacally laughingcalmly discussing the possibilities, let's get down to it.

Lenses take light and bend it. For the moment, we're gonna assume that all the light that reaches us from the Sun is parallel in direction. (It isn't, quite.) Depending on how much your giant space lens bends the light, your focused image could be anywhere from as large as it normally is (corresponding to a perfectly flat lens) to really small (corresponding to a really bulgy lens.)

Now, I'm gonna shy away from the awesome pyrotechnics that happen because that's not what you're asking. You're asking about what happens outside the focused image.

Recall from your childhood days of lighting things on fire with a magnifying glass. There's a shadow around the image of the sun (It's not actually a point.) where the light that would reach that spot is instead 'bent' and turned towards the focus point.

In effect, your answer is 'yes', there would be dark areas all around the focus point, as long as the lens is curved enough.

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  • $\begingroup$ I see what you mean. The sunlight falling on the lens is focused on Earth (which can be considered flat) and the light that otherwise would have reached the whole Earth is concentrated onto a certain part of the Earth. But won't this circular area be the same whatever the bulginess of the lens? Won't a weakly bulged lens give the same circular image on Earth. Of course, a flat piece of glass will do nothing, but you can't (well, of course you can) put this between the Earth and the sun. You have to place a lens with a varying bulginess (which is the smallest near the sun) between them. $\endgroup$ – descheleschilder Dec 8 '17 at 1:46
  • $\begingroup$ Ahem? It has been very strongly proven that the earth is NOT flat. $\endgroup$ – Jakob Lovern Dec 8 '17 at 1:48
  • $\begingroup$ that being said... No, the bulginess of the lens affects the angle of light entering it. This affects the angle of refraction, so that the lens concentrates light more intensely. $\endgroup$ – Jakob Lovern Dec 8 '17 at 1:50
  • $\begingroup$ Is it really true the Earth ain't flat? Doesn't a less strong lens concentrate the light also in a focus point (plane), which only lies further from the lens, so you have to place the lens further away from the (in this case as flat considered) Earth? $\endgroup$ – descheleschilder Dec 8 '17 at 9:36

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