yes a spotlight would be hard to explain,
but the sun is a floodlight with a broad light wave.
The sun moves all over our round, non spherical earth. this creates the amount of light per one area. Because it is a floodlight its rays can reach 1/2 of our disk earth at once.
It indireclty shines on the moon as well , and as the sun moves and the moon moves this creates the moon phases.
Ther is no consensus on the sunrises, sunsets.
I beleieve this occurs as the sun moves off the disk and its floodlight can no longer be seen.
Here's a little experiment you can try at home to prove your statement.
OK, the sun according to the FAQ, is 32 miles across and 3000 miles away. A ratio of 4/375. You could also as that the distance is 93.75 times greater than the size of the object. You claim the Sun is 32 miles across, and that the Earth is 24,900 miles across. That means the Earth is 778.125 times larger. Now, if we scale down the Sun to something a little more manageable for out little experiment, let's say, the size of a U.S. Quarter. The quarter measures 31/32 in across or .96875 inches across. Now, let's use our multiplier of 778.125 to figure out the size of our scale Earth. We get 753.809 inches, or for easier reference 62.817 ft. Now that we have our diameters properly scaled down, again, sorry for the mistake earlier, we can figure out our surface areas. The quarter's would be A=3.14*0.484375^2, which equals .7367 square inches, and the scaled down Earth would be A=3.14*31.4085^2, which equals 3097.59 square ft.
So, for this experiment, you need a light source no bigger that a quarter to illuminate at least half of a circle measuring 62.817 ft across. Go try it and get back to me. Please be sure video tape it so you can prove it's possible.