The familiar and beautiful phenomenon of the rainbow is produced by refraction, reflection and interference of sunlight by drops of falling water, such as rain or spray. As the ray of sunlight enters the drop of water, which acts as a tiny glass prism, it is refracted or bent from its course and spread out into its spectral colors. Reflection of these rays next takes place (once or twice, as the case may be) from the inside of the drop and a second refraction of the reflected ray takes place as it leaves the drop. The smaller the drops the more brilliant is the rainbow and the richer in color. The most brilliant rainbows are produced by drops between 0.2 and 0.4 millimeters in diameter. In addition to the primary bow, which has a red outer border with a radius of 42°, there is the secondary bow with a radius of about 51° and with colors reversed, the red being on the inner border; the supernumerary bows which are narrow bands of red, or green and red, appear parallel to the primary and secondary bows along the inner side of the primary bow and the outer side of the secondary bow. No rainbow arches ever appear between the primary and secondary bows, and it can be shown in fact, that the illumination between these two bows is at a minimum. The primary, secondary and supernumerary bows all lie opposite the sun in the direction of the observer's shadow and the observer must stand with his back to the sun in order to see them. The primary and secondary rainbow arches take the form of arcs of circles that have their common center on the line connecting the sun with the observer at a point as far below the horizon in angular distance as the sun is above the horizon. It is, therefore, never possible to see a rainbow arch of more than a semicircle in extent unless the observer is at an elevation above the surrounding country, under which circumstances it might be possible to see a complete circle formed by the rainbow. The highest and longest arch appears when the sun is on the horizon, and the greater the altitude of the sun the smaller and lower the visible arch. As the angular radius of the primary bow is 42° and of the secondary bow 51° and as the common center of the two circles is always as far below the horizon as the sun is above, it is never possible to see either primary or secondary rainbow when the altitude of the sun is over 51°, or the primary bow when the altitude is over 42°. For this reason rainbows are rarely seen at or near noon in mid-latitudes, since the sun is usually at an elevation of more than 42° at noon, especially in the summer season, which is also the most favorable season for rainbows, owing to the great likelihood of rain and sunshine occurring at the same time.