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Imagine a laser beam shining straight up from the surface of the earth. As the light gains altitude it encounters less and less air and soon no air at all. My question is when it leaves the refractive index of air will it change its direction?

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In a typical gas, the index of refraction depends on the density, so it will be changing direction more or less continuously - unless the direction of propagation is always perpendicular to the surfaces of constant density (roughly, pointing straight up - but even then density fluctuations would cause changes in direction).

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