ir has a small, usually negligible index of refraction. It is 1.0002926. This ca

Question

ir has a small, usually negligible index of refraction. It is 1.0002926. This causes the Sun to actually be below the horizon when it appears to be just on the verge of sinking below it. Suppose you are on the sea-shore watching the Sun apparently sinking into the ocean. When only its upper tip is still visible, by what fraction of the diameter of the Sun is that tip actually already below the surface? As an approximation, take the earth's atmosphere as being of uniform density out to a thickness of 9.000 km, beyond which there is no atmosphere. This means that, with the Earth's radius being 6400. km, your line of sight due West along the ocean surface to the horizon will intersect this "upper surface" of the atmosphere at about 339.5 km from your eye. (If you enjoy trigonometry you can check this figure for yourself.) (The diameter of the sun subtends 0.5000 degrees at your eye.)

Explanation / Answer

Hello

The ray of the sun within the air, the radius os the earth, and the radius of the earth + atmosphere
make a right angled triangles with base (6400+ 7.5), and sides 6400 and 309.9 km.
The sine of the angle a between the sun ray with the 6407.5 km base is
sin(a) = 6400/6407.5. --> angle a = 87.2275

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