When it has been raining, and the Sun is behind an observer, the conditions are right for the production of a remarkable optical phenomenon : the rainbow.
Sunlight, which appears to us as being white, is actually a mixture of several colors, the number of which is often given as 7.
A prism decomposes white light via refraction, with the path of each color being bent at a different angle, the angle of which increases as we go from red to violet.
Just as in a prism, a raindrop refracts the white sunlight, but its spherical shape changes the paths of the refracted rays. Light is refracted when it enters the raindrop, then reflected from the rear of the drop, then refracted again when it exits back into the air.
The ultimate angle between the rays of the Sun and the perceived image is around 40°, but with a slight difference for each color: 40.5° for violet …42.4° for red.
At any given moment, the observer’s eye sees only one part of the light coming from each drop.
Thus, for a drop that disperses all of the colors, only the red rays reach the observer’s eye, and he sees only red.
A raindrop that is located lower down also disperses all of the colors, but only the orange rays enter the eye…
… and so, as a result, the observer sees all of the colors of the rainbow, but different colors seem to come from different areas of the sky.
Mathematical analysis shows us that the phenomenon thus observed is an arc of a circle whose center lies below the horizon.
Sometimes a second reflection occurs in the interior of a raindrop. In this case, one sees a second, but less bright, rainbow, outside the primary one, at an angle of 50°.