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I am wondering whether it is possible for a guy in a deep well to see the stars in the daytime.

Now the background is dark. So might the stars be visible?

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    $\begingroup$ As the answer says, the sky background still isn't dark. $\endgroup$ – Carl Witthoft Mar 13 '17 at 12:42
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No, because being in a deep well doesn't make the background dark.

The reason we can't see stars in the daytime is the atmosphere, which scatters sunlight in all directions such that along every sightline from the ground toward the sky you receive much more photons from the Sun than from a star.

That is, the photons that makes it impossible to see Vega, for instance, are the photons from the Sun that make their last scattering event at a molecule lying between you and Vega. Being in a well blocks the star- and sunlight from other directions, but lets through both star- and sunlight from Vega's direction.

Like this:

well

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I have a photograph taken with an infrared camera (scattered blue light filtered out) from within a medieval tower open to the sky. The stars ARE visible.

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