The ancient maxim "Blue are the hills that are far away" articulates a common perception that the unattainable invariably seems more attractive that what we may have readily to hand. But on a sunny, hazy day, it is also true in a literal sense, as many of the poets testify. A.E. Housman, for example, asks us:
What are those blue-remembered hills;
What spires, what farms are those?
Milton is a little more obscure when he recalls events "by slow Meander's margent green and in the violet-embroidered vale"; thereby, when you get his drift, contrasting the greenness of the river bank with the bluish hills that form its valley. But Thomas Campbell was nearest the mark when he told us that:
'Tis distance lends enchantment to the view,
And robes the mountain in its azure hue.
The explanation lies in the scattering of light waves by tiny particles suspended in the atmosphere. Waves of any kind are often obstructed by obstacles in their path, just as a boulder interferes with water waves, sending wavelets off in many new directions.
Tiny dust particles in the air, and indeed the very molecules of the air itself, are efficient scatterers of the shortest light waves, those at the blue end of the spectrum. As a consequence, the blue light in a ray of sunshine is diverted in many different directions as it passes through the atmosphere; the remaining colours with longer wavelengths - like red and orange - continue on their journey ground-wards unaffected.
As you look at a mountain in the distance you see, naturally enough, the mountain itself which, typically, may be green or brown. But superimposed on this image is another source of light: some of the blue from rays of sunlight passing through the air is diverted in your direction by the process of scattering.
It is this scattered blue light which lends the scene its characteristic colouring. Moreover, the greater the distance to the mountain, the more air there is in between to scatter light in your direction, and so the bluer the distant hills will seem to be; sometimes a deep enough shade to merit being described as purple.
We also notice that at the beginning or end of a sunny day the atmosphere, again because of scattering but in a different way, tends to acquire a pink or orange tinge. It is therefore in the middle of the day that the far-off hills are at their very bluest.