It seems your question comes down to "Why does light at least somewhat follow the curvature of the earth?".
The answer is indeed refraction. Light has different speeds in different transparent substances, always slower than in vacuum. From this differing speed, you can show that a light beam is bent at the boundary between substances with different index of refraction, which is the ratio of how much light slows down in the substance compared to vacuum. Camera lenses, eyeglasses, etc, harness this principle deliberately.
The speed of light in air is close to that in vacuum, but not exactly the same. Put another way, the index of refraction of air is almost 1, but not quite. Furthermore this index of refraction varies with the density of the air. To convince yourself of this, imagine the limiting case where you measure index of refraction of air as the pressure is gradually lowered. When it gets to 0, the index of refraction must be 1 by definition. The index of refraction of air therefore varies smoothly as a function of pressure.
Now think of the air envelope around the earth. Obviously there is a pressure gradient with altitude. When you get high enough, the atmosphere is gone and you have only the vacuum (almost) of space. In this case there isn't a sharp boundary like there is when light enters a glass lens. However, the gradient still bends light, in this case smoothly over some distance, as apposed to abruptly at the air/glass boundary in the lens example. This vertical pressure gradient, and therefore index of refraction gradient, causes light to bend a little when shot horizontally thru the atmosphere.
However, there is more to it than this general effect. The atmosphere is not uniform at any one altitude. As you know, there is wind, pockets of hot and cold air, rising thermals, cold downdrafts, and lots of phenomena that are much more significant locally than the general decrease in pressure vertically. The air can have different layers at different temperatures, and the interface between layers can be much more abrupt than the general trend of decreased pressure with altitude.
Shooting a light beam with the right atmospheric conditions can exhibit much more bending than in the general average case. A mirage is a good example of this. Light from the horizon is refracted by the relatively sharp boundary at the top of a thin hot layer of air warmed by the ground. From far enough away to that the light is at a very glancing angle, you "see" sky light reflected off of what looks like the ground. This gives the visual impression of a lake, since a lake would similarly reflect sky light in normal cases even when there are no special atmospheric effects.
In the case of a mirage, light is actually bent upward. Light can just as well be bent downward using similar boundaries of layers in the atmosphere. It depends on the position of the emitter and receiver relative to the index of refraction gradients in the atmosphere.
If you were to carry out these experiments on the moon, which has no practical atmosphere for this purpose, light beams would indeed to "straight". You won't see mirages on the moon, for example.
Apparent size is not measured as an ordinary size, in meters. It is actually an angle, so it is measured in degrees or radians.
See this picture:
The object on the left is the eye. Looks like as the object moves further, the angle becomes smaller.
That is what is called perspective.
Sometimes people try to compare apparent size (solid angle) and real size, but that makes no sense because they have different dimensions. For example, I've been asked:
Is the Moon bigger or smaller than a 1€ coin?
The answer is that it is much, much bigger: about 3000 km vs 2 cm. What the question is trying to ask is compare the apparent size of the Moon with the real size of a coin, and that makes no sense. You should compare the apparent size of the Moon with the apparent size of the coin, but then you should say what distance the coin is.
For reference, the Moon apparent size is about half a degree. That is about the size of your thumbnail, with the arm extended. It does not matter if your hand is big or small because a big hand will also mean a big arm!
Best Answer
In the aquarium tunnel the fish appears smaller because the acrylic with the water behind it creates a diverging lens. You can see in the ray diagram below that fish inside the aquarium appears smaller(you outside will see a diminished or smaller virtual image). The sides of the tunnel taken approximately cylindrical( that is in the arc of a circle).
Using small angle approximations the size of the fish decreases by approximately 30%(factoring in refractive index of water and of acrylic where the refractive index of acrylic cancels out in the mathematics) if you calculate the angle of divergence. Thus the fish do appear smaller in such an arrangement for viewing in a tunnel.
Note: You can think of this scenario like the opposite of a fish bowl where fish look larger inside the bowl but here it's like you are inside the fish bowl and hence the outside world(fish in aquarium) looks smaller by the law of reversibility of light.