Mnoranjan Kumar

The simplest way to define a harmonic progression is that if the inverse of a sequence follows the rule of an arithmetic progression then it is said to be in harmonic progression. This simply means that if a, a+d, a+2d, ….. is an A.P. then 1/a, 1/(a+d), 1/(a+2d), …… is an H.P. For example, the series 1 +1/4 +1/7 +1/10 +..... is an example of harmonic progression, since the series obtained by taking reciprocals of its corresponding terms i.e. 1 +4 +7 +10 +... is an A.P.

Two physical phenomena are at work within a rainbow: refraction and reflection. Refraction occurs each time light passes across a boundary from one substance to another, such as from air into water. As light crosses that boundary, the rays bend at different angles depending on the wavelength (color) of light. This is the familiar prism effect wherein "white" sunlight is broken into a spectrum of different colors from red to blue-violet. The same thing that happens in a rainbow: white sunlight enters a raindrop and is broken into different colors heading in slightly different directions. The light is then reflected (and magnified) off the back of the raindrop and passes back into the air again, in the process being further refracted. Double Rainbow (outer arc on right) Let's pick a single raindrop in the BLUE band of the arc. The blue light is but one part of the spectrum of colors - each shining out from the raindrop at a different angle. Blue is shining our direction, but the other colors shoot out in different directions and therefore we can't see them from where we stand. Now look at an adjacent raindrop: it's also shining blue light at us. In fact, all of the nearby raindrops appear blue from where we're standing. But if we look at a single raindrop in the RED band of the arc, only the red light is shining our direction. In between blue and red, we find "all the colors of the rainbow" refracted and reflected from countless raindrops in just such a way that they shine our direction. Beyond the edge of the arc, where we see no color, the raindrops may be emitting colored light but none shines in our direction. Double Rainbow Photo by Bob Peavy Under certain conditions, some of the light will bounce off the inside of the water droplet more than once, exiting at a different angle. This produces a weaker, secondary arc known as a double rainbow. Bob Peavy has captured this phenomenon in the images above and left. Note the colors are reversed in the secondary rainbow. In theory there are additional rainbows (third, fourth) but those are too faint to see.