Some people have been asking why the sun's spotlight changes shape over the year. This can be answered by looking into the mechanics of the spotlight itself. The base question, "how is it that the earth is not at all times illuminated all over its surface, seeing that the sun is always several hundred miles above it?" may be answered as follows:--
First, if no atmosphere existed, no doubt the light of the sun would diffuse over the whole earth at once, and alternations of light and darkness could not exist.
Secondly, as the earth is covered with an atmosphere of many miles in depth, the density of which gradually increases downwards to the surface, all the rays of light except those which are vertical, as they enter the upper stratum of air are arrested in their course of diffusion, and by Snell's Law bent downwards towards the earth; as this takes place in all directions round the sun--equally where density and other conditions are equal, and vice versâ--the effect is a non-uniform area of sun-light.
For a striking example of Snell's Law we simply need to put a straw into a glass of water:
As we can see, the light from behind the glass is bent downwards as it passes through the thick medium of the water. While this is an extreme example, it shows that light is malleable, able to bend and conform based on existing conditions. When the light of the sun moves from the vacuum of space into the atmosphere of the earth it is gradually compelled downwards into the surface. The refractive index of air is a bit less than water, and so the effect will me more gradual, taking place over tens of thousands of miles instead of abruptly like the above image.
This considered, lets designate some facts.
Fact: Cold air is denser than warm air, and has therefore a greater refractive index.
1Fact: The sun is farther from the earth in its Northern Annulus and closer to the earth during its Southern Annulus.
2We're just coming into a summer and right now the sun is positioned over the equator, the majority of its warmth spread over the ring of the equator. The sun is at it's middle point between hemispheres. The atmosphere in this area around the equator is at its highest temperature and therefore, since warm air has less of a refractive index than cold air, light can progress further through the atmosphere without bending towards the ground. This results in the spotlight of the sun conforming to the shape of the hottest areas. The end result gives the spotlight of the sun an oval shape taking up approximately one half of the earth:
When the Sun is over the North and at its highest altitude the spotlight is small and circular. This is because the sun is far from the earth and not heating the atmosphere up very much. At this time the entire Southern Hemisphere is in its Winter, and since cold air is denser than warm air, the refractive index is higher and light cannot proceed without being redirected into the earth. Since the earth is colder, the light is restricted to a small circle where summer exists in the North.
When the sun is over the South and close to the earth the sun is heating up the Southern Hemisphere, giving the spotlight a wide crescent shape. The shape is a crescent because when the sun is over the South it is winter in the North and the sun's light cannot penetrate the density of the Northern Hemisphere's winter.
The shape of the spotlight defines the time it will take for the sun to set. If the spotlight is small, the sun will appear to pass over the earth quickly. If the spotlight is large, the sun will take appear to take a longer time to pass over the earth. In the above illustration the Sun's spotlight is neither small or large - but at it's median - taking up approximately one half of the earth's surface and giving us 12 hour days.
1 Second paragraph in the
Wikipedia article on Mirages2 See the
Sun's Analemma which demonstrates the height of the sun over the course of the year.