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The old theory about seeing stars during the day if you stand i the bottom of a well or chimney is proven wrong because the atmosphere scatters the sunlight and makes it too bright to see the stars through.

But what about during the night in cities? Could it work the other way around and sufficiently block out the city light pollution, making it possible to see stars as if it was a black sky even though you were in the middle of a city? And if so what would be the minimum height acquired from the well/chimney and how big a diameter would it be able to have while still blocking out the light pollution?

Sensebe
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From a physicist point of view it does not help! Pollution is the reflection of light in the atmosphere rather then lights around you. When you step underneath your chimney, you will still see all the reflection of the light in the atmosphere right above you.

BUT: You will of course have a better view of the stars, as your eyes don't have to adjust to the lights around you, thus being more sensitive for any light coming from the stars.

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Light pollution (as Chris White said in the comments) is less about glare from lights directly beaming into your eyes and more about the atmosphere itself being lit up and essentially drowning out the stars. The contrast between a light polluted sky and stars is too low for our eyes to make the stars out.

One way to get around this is to use a filter. If you choose a filter that focuses on a specific wavelength of light that stars produce a lot of (which can vary from star to star) then you can increase the contrast with the sky and possibly make stars out even in a light polluted sky. Unfortunately, although filters are useful to increase contrast of a star against the sky they will also cut down the overall brightness (or flux) coming from the star, so you risk making the star too dim to see even against a perfectly black sky.

NeutronStar
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Light goes as far up as the atmosphere. Hence, To block light pollution you would have to build a tower many miles high to make it seem like there is no light pollution.

Shadow
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