Wave phenomena

We shall start with some very simple facts about light waves. The wavelength and frequency are closely related, in fact they are inversely proportional to each other viz, the higher the frequency the shorter the wavelength. This simple fact is given by
The equation for electromagnetic waves : λν=c , where λ is the wavelength, ν is the frequency and c is the speed of light.
The analysis of wave phenomena fits properly in the mathematical topic of non-linear analysis. Ever since physicists Huygens and Hertz began to understand light waves there is an ever increasing apetite to understand waves better.This is partly due to the practical considerations of image processing and VFX and also partly for pure mathematical fascination.
 The details of how rainbows form are fascinating, too. Light is refracted upon entering and exiting raindrops, and reflected within raindrops, sometimes more than once. The angle of refraction and thus the position of the rainbow--not a fixed place but at an angle of elevation of about 42 degrees from the line connecting your eye to your head’s shadow--can be figured out using trigonometry. Because different colors of light have different wavelengths, they are refracted at different angles, which produces a rainbow (or two).
If you look closely, you’ll see lighter colors inside the inner violet band (inset), which appear because of the interference of light waves, with some waves reinforcing each other. The explanation for these bands isn’t obvious and they weren’t accounted for in early theories about rainbows. Proving that these lighter bands should appear required the wave theory of light and their precise description involved an integral, (the Airy integral) that was numerically evaluated using infinite series. Curiosity about rainbows has led to many other discoveries in mathematics and physics, including “rainbows” formed by scattered atoms and nuclei.