I need to figure this out
Yes, I have seen this before when viewing the Rocky Mountains of the some of the remote areas of eastern Banff National Park in the west from the area about thirty miles south-east of Red Deer, Alberta, Canada On certain days, you can see the mountains, somewhere between one hundred and two hundred miles away, much more easily than on others, due to the mirage effect which happens in some kinds of weather.
Am I sure there was really an effect -- that I didn't just imagine things? Absolutely so, because normally even on a clear day the mountains don't normally appear as high above the horizon as they did on certain days, when we concluded a mirage must be at work. The apparent height of the mountains viewed from the ground on those special mirage days was a little shimmery, but much more like their apparent height when viewed from a light aircraft flying at several hundred feet altitude at the same location . Conclusion: something bent the light downward.
Comparing what happens to a light ray exiting from a slow medium to a faster one, such as from glass to air, we'd use Snell's law to see that the rays such that their path is always closer to the vector that is normal to the interface in the faster medium than in the slower medium. In this case, perhaps the interface was hotter air rising off of a surface such as pavement that more easily absorbed the sun's rays than everything else around it.
Let's make this a problem to solve using Snell's law:
If the same rays from mountains 200 miles away that would normally hit an observer in an airplane five hundred feet above an observer on the ground are instead hitting the observer on the ground, due to a sudden change in the index of refraction of air as the rays pass from the cold region near the mountains into a cylindrically vertical region of warmer air that extends over the entire area within 50 miles of the observer, and if the index of refraction of air varies with temperature according to the following relation, n = 1.00 + 0.01(T-300), where T is in K, find the temperature difference necessary to cause the observer to see those rays.