How a Rainbow Forms
A rainbow is a combination of water droplets and light, that spreads out into an spectrum of colors. You will see a rainbow when the sun is behind you and there is moisture in the air in front of you - this is important to remember when understanding how a rainbow is formed.
Light Refraction
Light can bend. When light hits a surface it will bend over it, through it or around it. It changes speed and direction. When light hits a transparent material, such as glass or a water droplet at an angle, it refracts (bends) and disperses through the droplet. The arc of the rainbow appears by the angle the sun hits the droplet, the bending of light through millions of water droplets causes the colours to be shown in a semi circle. This process is called "Snell's Law of the Refraction of Light." See the image below for a demonstration:
Light Dispersion
White Light
We see light as white, but it is made up of many colours. When the beam of light passes through the water droplet it slows down and spreads out or disperses, separating each colour that makes up white light as a spectrum of colours. The colours we see in a rainbow are : red, orange, yellow, green, blue, indigo and violet.
There are other colours, but we can't see them through our human eyes - even infra-red and ultra-violet! The index of refraction is the measure of speed of the wavelength of colour. Each colour has a different speed of refraction. You will see the colours of the rainbow in the same particular order because of this speed.
This image below shows light passing through a glass prism, which illustrates what happens when light passes through water droplets. You can see that the beam of strong white light hits the glass and reflects up (the thin white line) and it also refracts through the glass, dispersing out the other side in a spectrum of colours.
Summary : A rainbow is therefore millions of water droplets, each one refracting and dispersing sunlight. The sun is hitting every droplet at a low angle and is situated behind you as you look at the rainbow. The arc of the rainbow is caused by the way the light is bending through the droplets.
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