The index of refraction for Air is only slightly above 1. (1.0003).
1 is a vacuum.
This means that air is only slightly denser (optically) than nothing. How far can one see light do you think?
80 miles at sea level. It really depends on conditions. The area around New York is so polluted that visibility is under 25 miles. Contrarily, people have reported making out the outlines of distant mountains 100 - 150 miles away from the top of Mt. Everest. But the thinness of the atmosphere is different up there.
I don't understand what you're getting act with the index of refraction. That's not being discussed.
This statement contradicts itself, and we've had this discussion before. Something cannot diffuse and magnify light at the same time. If the atmosphere built up like a fog after 80 miles or so, then all you would see of any lights, including the sun, would be a hazy glare, especially when the sun was near the horizon. What exactly do you mean by "the light catches onto the atmosphere?"
200 feet of fog may block out the light of a car behind it, but when that car turns on its headlights the light will permeate the fog. The light has
caught onto the atmosphere and can travel further than normal light rays, in addition to magnifying its size. This is what the sun does, albeit on a larger scale.
The light is scattered in the fog example because the granularity of the surface medium is dispersed at such a close range. In the case of the sun, there are many more molecules to shine upon, as the sun is thousands of miles away. This results in a higher resolution and sharper image.