The reason why the rainbow is curved is because all the angles in the water drop have to be just right for the drop to send some sunlight to you, standing on the ground. ......................................
A rainbow is round because the process is based on angles. Light from the sun hits the little water droplets after a rain. The water droplets act like little prisms. Different colors are sent out at different angles. The sun must be behind you. Imagine a narrow triangle. The narrow angle is at the water drop. One side points toward the sun. One side points toward your eye. The drops for which this device works form a circle. The center of this circle lines up with you and the sun. If the Earth were not in the way, a rainbow would be a complete circle. This is why you can never find "the golden pot at the end of the rainbow". A rainbow is really a complete circle.