Course 7.3Lesson 1 of 3
The air gets denser toward the ground, so a ray of light from space bends gradually as it comes down. This is atmospheric refraction. It makes stars twinkle, it makes the Sun seem to rise about two minutes early and set about two minutes late, and it makes the Sun look flattened at the horizon.
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Look at a star on a clear night. Its light seems to flicker. Look at a planet such as Venus or Jupiter. Its light is steady. Why? To answer this, we need to study how light goes through the air.
The air around the Earth is thin at a great height and dense near the ground. We can think of it as many thin layers. The upper layers are optically rarer, and the lower layers are optically denser.
A ray of light from a star goes from layer to layer, and at each layer it goes from a rarer to a slightly denser material, so it bends toward the normal. The normal is the vertical line. The path of the ray is a curve, and it is more vertical near the ground than it was at the top.
The eye follows the last part of the ray back in a straight line. So the star seems to be higher than its real position.
You should find that a star overhead is not moved at all, and a star near the horizon is lifted most: its light crosses the layers at a slant. In real air the lift is tiny, less than a degree, but it is enough to matter at sunrise and sunset.
The air is not still. The layers move all the time, and their density changes from moment to moment. So the apparent position of the star shifts a little, and the amount of light that enters the eye changes. The star seems to jump and to flicker. This is twinkling.
A star is so far away that it is a point source of light. The change of the path of its light is large compared with its tiny size, so the effect is strong.
A planet is much closer, so it is an extended source. We can think of it as a large number of point sources. The flicker of one point is cancelled by the opposite flicker of another, and the total light that enters the eye stays steady. So planets do not twinkle.
The same idea works at the horizon. When the Sun is a little below the horizon, its rays are bent by the air, and they reach the observer. So we see the Sun before it really rises, and after it really sets.
We see the Sun about two minutes before the true sunrise, and about two minutes after the true sunset.
On a certain day, without the air, the Sun would rise at 6:05 and set at 18:15. When do we see it, and for how long?
At sunrise and sunset, the Sun looks flattened, like an oval. The rays from the lower edge of the Sun pass through more air than the rays from the upper edge, and they are bent more. So the lower edge is lifted more than the upper edge, and the height of the disc seems smaller than its width.
The program finds how much the air lifts a star, for real air with , using the same layer idea as the simulation.
Try each one on your own first. If you are stuck, open a hint. Then check with Show the answer.
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