After rain fall the humidity level of air increases and there is large concentration of tiny droplets of water in the air to refract sunlight. Rainbow forms when sunlight hits the water droplets suspended in the atmosphere and undergo total internal reflection. When the sunlight comes out of the drop it disperses, where the drop acts like a small prism. This is why we see rainbow after rainfall.
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A rainbow is an optical and meteorologi cal phenomenon that causes a spectrum of light to appear in the sky when the Sun shines on droplets of moisture in the Earth's atmosphere . It takes the form of a multicoloured arc . Rainbows caused by sunlight always appear in the section of sky directly opposite the sun.
In a "primary rainbow", the arc shows red on the outer part, and violet on the inner side. This rainbow is caused by light being refracted while entering a droplet of water, then reflected inside on the back of the droplet and refracted again when leaving it.
In a double rainbow, a second arc is seen outside the primary arc, and has the order of its colours reversed, red facing toward the other one, in both rainbows. This second rainbow is caused by light reflecting twice inside water droplets.
Light from the sun appears to be colourless but it is really made up of all seven visible colours (red, orange, yellow, green, blue, indigo and violet). When the "white" sunlight enters a raindrop it breaks up into the various colours (due to a process called refraction) and bounces back out of the drop towards your eyes when it reflects off the rear surface of the raindrop.
For this to occur the sun has to be shining and you have to be between where the sun is in the sky and the rain or mist droplets are located. You can make your own rainbow with a garden hose set to mist on a sunny day or by using a prism,