Rainbow 

A rainbow is one of the most beautiful meteorological phenomena in Nature, which includes the spreading of colours through reflection, refraction, and dispersion of light, typically sunlight, through water droplets in the atmosphere. 

1.0Introduction to Rainbow 

A Rainbow consists of seven semi-circular arcs forming in the sky after a rainy day. It is formed when the water droplets in the environment interact with sunlight, giving rise to the phenomenon called dispersion. 

2.0Conditions for the Formation of a Rainbow 

• Presence of Water Droplets: The prerequisite to the formation of a rainbow is that there must be tiny droplets of water suspended in the atmosphere. These can act as prisms.
• Sunlight: This is the source of light, and it must be behind the observer for a rainbow to form.
• The Angle of View: The angle of view in a rainbow refers to the angle through which the colours of the rainbow appear to an observer. The angle depends upon the wavelength of the light. The angle is calculated from the angle of refraction at which light leaves the water droplet after it has been dispersed and reflected.

3.0The Sequence of Colours

The dispersion of light is the reason behind the formation of the spectrum of colours that are typically arranged in the sequence of VIBGYOR (Violet, Indigo, Blue, Green, Yellow, Orange, Red) in the order of increasing wavelength and from the inner edge(Violet) to the outer edge(Red). 

4.0Types of Rainbows

1. Primary Rainbow: This is the major rainbow that is observable following a rain. It forms by a single internal reflection within the water droplets. Colors will appear in this order: Red, Orange, Yellow, Green, Blue, Indigo, and Violet.

2. Secondary Rainbow: A secondary rainbow is thinner, and it appears outside of a primary rainbow. This is the result of two internal reflections inside the droplets of water. The colour appears in reverse order - the outer edge is violet colour on the outside, whereas the inside is red.

5.0Science Behind Rainbow

Refraction

The bending of light travelling in a rarer medium and entering into a denser medium and vice versa is known as refraction. When sunlight enters a water droplet, it slows down and bends because of the change in the medium from air to water. The amount by which different colours, or wavelengths, of light bend, varies because the refractive index of water changes with wavelength. This effect is responsible for the process of dispersion.

Dispersion

The bending of light on different angles due to refraction forces the sunlight to separate in its seven component colours i.e. red, orange, yellow, green, blue, indigo, and violet, this process is known as the  Dispersion of light. 

Reflection

Finally, after refraction and dispersion inside the droplet, light is reflected by its inner surface. The internal reflection makes the light return in the direction of the observer's eye.

Refraction Again

When the light travels out of the droplet, it undergoes another refraction at the water-air boundary. The light exits at the angle at which the rainbow exists. The second refraction separates the colours further.

Formation of the Rainbow

Each colour has a different wavelength; hence, each colour is refracted at a different angle. Red light would be refracted at approximately 42° while violet would be refracted at around 40° to make the circular arc of a rainbow.

Mathematical Explanation 

The angle of deviation $\left(\delta \right)$ of the light coming out from the droplet after internal reflection is affected by the wavelength of the light and the refractive index of the water. The mathematical representation of this is: 

$sin\theta =\frac{n}{v}$

Where, 

• θ is the angle of refraction,
• n is the refractive index,
• v is the velocity of light in the medium.

6.0Also Read