rainbow is the exhibition of dispersion, refraction and reflection of light taken together.
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Rainbow is the exhibition of diespersion, refraction and reflection of light which has been described below in details: White” light from the sun comprised of many different wavelengths enters a raindrop.
Water has a refractive index different than that of air; so as the white light enters the raindrop, it refracts.
However, the angle at which it refracts is determined by the wavelength of the light; and so, different wavelengths refract at different angles.
This is known as “dispersion”; a “dispersive medium” is one whose refractive index (which determines how much the light bends) is dependent on the wavelength of the light.
The light, now “split” into a spectrum of different wavelengths travelling at different angles, then travels through the water droplet until it hits the other side.
If it does so at the correct angle, the light will reflect from the far side of the droplet, rather than simply refracting out the other side.
This is “internal reflection.”
“Total internal reflection” is when all the light is reflected, and none passes through - this isn’t what actually happens in a raindrop, some light does pass through, and in real life you just end up with a high concentration of different wavelengths of light at different angles rather than complete splitting, but that’s pedantry.
The light will then travel back through the droplet and refract out of a different point.
However, as it is split up into this “spectrum” of light now, all travelling at different angles out of the raindrop, only one of the wavelengths will come out at the correct angle to hit your eye.
The others will go to the side of or above/below your eye.
They’ll “miss” your eye.
You’ll therefore see a “band” of that particular colour through the sky, in an arc shape.
The arc shape is because you need to be at the right angle to the raindrop to receive that colour of light, and that angle will correspond to an arc of points equidistant from you - in a circle shape.
So overall, this forms a cone, with the tip at your eye and the circular base being the arc of the rainbow.
Slightly below this band, you will get the same phenomenon occurring, but all the angles will be a little different - so the light that ends up hitting your eye instead of missing corresponds to light of a slightly different wavelength, as that will have refracted at a slightly different angle.
This then gives a band of a different colour, adjacent on the colour spectrum to the colour of the first band (e.g. blue, if the first band was violet/purple.)
This obviously occurs throughout a range of space, giving you the entire colour spectrum next to eachother in the familiar “band” structure of a rainbow.
This range of space is narrow, however - which is why the entire sky isn’t a bunch of rainbows, you just get one (or maybe two.)
The range of space corresponds to the narrow range of angles at which internal reflection will occur within the water droplets.
We don’t get a rainbow without the internal reflection as, although the light will be split if it just passes through the water, you’ll get a lot more “mixing” of the light again, washing out the striation of the different colours that forms a rainbow.
This is why you’ll only see a rainbow when the sun is behind you.
It’s also why the rainbows only occupy a particular narrow arc as described above - if the whole process didn’t need to occur through the narrow range of angles in which internal reflection occurs, then you’d get full rainbows to your eye in many locations throughout the sky and it would all cancel out anyway.