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I have read that it is a myth that you can see stars in daylight if you stood at the bottom of a well, however, if you stood at the bottom of a well at night, or built a long non-reflective tube and pointed it to the sky, would you be able to see more stars through the tube in a light polluted area?

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The stars are almost point-like light sources with a full width half maximum (FWHM) angular extent of 1-3 arcseconds, caused by atmospheric turbulence, depending on the quality of your viewing site. The well-adjusted human eye has a best angular resolution of only about 15 arcseconds. (Which can be estimated as $\lambda/D$ in radians, where $\lambda$ is $\sim 500$ nm and $D \sim 8$ mm is the diameter of the pupil.

Thus when you look at a star, its light is spread on your retina to occupy the same area as a patch of sky that is of order $100$ times the surface area.

Given that the daylight sky has a brightness of around 3 mag per square arcsecond (depending on how near the Sun you look and time of day etc.) then you can understand, just from a signal-to-noise pint of view, that the signal coming from the sky totally overwhelms even bright stars.

This calculation isn't going to be changed by looking at the sky from the bottom of a well.

The only way you could see stars during the daytime is to increase the angular resolving power of the eye by a factor of 10 or so, or better still, look through an 8 cm telescope, since that is exactly what a telescope does in addition to gathering more light.

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I have not heard of this myth, but you can find it on Snopes:

https://www.snopes.com/fact-check/star-search/

Based on the discussion there, I would think that yes, you might be able to see more stars through a tube. You would be blocking some light sources, particularly local ones (depending on the size of the tube), but as discussed in the Snopes post, most of the skyglow would still be present. Like the daytime case, I doubt the effect would be significant enough for you to actually notice. Perhaps, if you knew a particular star was just below the level of your local observation conditions, you migth be able to increase the chance of observing that particular star with a long enough tube. However, I don't think the experiment is really worth performing.

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