Magnification of the Sun at Sunset
Q. If the sun is disappearing to perspective, shouldn't it get smaller as it recedes?
A. The sun remains the same size as it recedes into the distance due to a known magnification effect caused by the intense rays of light passing through the strata of the atmosphere.
From Chapter 10 of the book Earth Not a Globe we read:
"IT is well known that when a light of any kind shines through a dense
medium it appears larger, or magnified, at a given distance than when
it is seen through a lighter medium. This is more remarkable when the
medium holds aqueous particles or vapour in solution, as in a damp or
foggy atmosphere. Anyone may be satisfied of this by standing within a
few yards of an ordinary street lamp, and noticing the size of the flame;
on going away to many times the distance, the light upon the atmosphere
will appear considerably larger. This phenomenon may be noticed, to a
greater or less degree, at all times; but when the air is moist and
vapoury it is more intense. It is evident that at sunrise, and at sunset,
the sun's light must shine through a greater length of atmospheric air than
at mid-day; besides which, the air near the earth is both more dense, and
holds more watery particles in solution, than the higher strata through
which the sun shines at noonday; and hence the light must be dilated or
magnified, as well as modified in colour."
- Samuel Birley Rowbotham
The next time you observe the sunset notice how the sun is much hazier, diluted, and less intense than when it is overhead at noonday. This is a telltale sign that its rays are passing through a thick horizontal atmosphere, much like the light rays from a distant street lamp. The sun's intensity is so diluted when it is low in the sky that it is possible to look directly at it without squinting.
If you've ever seen a city at night you would know that distant light sources appear magnified from afar because they are shining though an atmospheric medium. The farther you move away from the source, the more medium you put between you, the more magnified the lights appears. As you move towards the source the magnified lights shrink in appearance. As you move away the lights grows in diameter again.
Consider the picture to the right. You will immediately notice upon looking at the image that the distant lights in the scene appear magnified and intense, particularly the white ones in the upper left of the image. You should note that most of the the lights in the background are about as big as the lights in the foreground. This is entirely contradictory to what one would expect. The background lights are much farther away and the distant bulbs are all smaller than a single pixel of the screen. The orange lights maintaining their size in foreground and background is a great example of the magnification effect of the atmosphere balancing out the natural shrinking to perspective.
As an analogy for the enlarging of the sun at sunset, lets imagine that we are in a dark room with a flashlight. We shine the light upon the wall, creating a distinct circle of light. If we walk backwards and recede away from the wall the spot of light grows in diameter. When we walk towards the wall the spot of light becomes smaller again. The same effect happens with the distant sun at sunset. Instead of a solid surface like a wall, however, the rays of light are shining upon the semi-transparent fog of the atmosphere between the observer and the sun. The natural shrinking of the sun due to perspective is counteracted by the enlarging effect of its light upon the horizontal strata of the atmosphere between you and the light source. This is how the sun's diameter is maintained throughout the day.
Headlight Example
The light from these incoming headlights are a constant size down the highway as far as the eye could see.
Notice how it is only the intense headlights of the cars on the incoming lane which are magnified. The headlights on the lane coming towards us are all the same size. The intense light from the headlights have caught onto the atmosphere between the source and camera to create a magnification of the light. This magnification increases with distance, allowing the headlights to appear the same size down the entirety of the lane.
In contradiction, the red tail lights of the cars driving away from the camera are not intense enough to catch onto the atmosphere and are appropriately shrinking into the distance.
Distinctness of the Sun
Q. Shouldn't the sun get blurrier if it is being magnified?
A. The sun actually does get a bit fuzzier when it is at the horizon compared to overhead at noonday.
Q. But shouldn't the sun get 4x blurrier if it is increasing its diameter by 4x, for example?
A. No. You are assuming that the sun is being magnified in a similar method as a magnifying glass, where blurriness occurs as a ratio with distance. This is incorrect. The magnification of the sun occurs through a projection. A projection of light is occurring upon the atmosphere between the sun and observer. And as anyone who owns a Projection TV knows, the image does not get blurrier the further you stand from it.