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The atmosphere appears bright because of scattering of light whereas space appears dark due no atmosphere to aid scattering.

Is it possible to demonstrate it with such darkness in a huge vaccum glass bulb?

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The bulb needs to be big enough that the scattering matters for any visible effect to show up. This size scale is typically at least kilometres for pure air (consider how far away something has to be before it starts to get a bluish colour perspective). So a multi-kilometre vacuum bulb would likely create an unusual clarity of objects on the opposite side when you compare seeing them through air. In a more misty, smoky or polluted environment the bulb might of be far smaller.

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