Refraction and Dispersion of Light

Isn't it true that rainbows are the most beautiful natural phenomenon on the planet? It appears to be flawless! Isn't that so? Have you ever noticed that rainbow-like events can also be seen in prisms and crystals? What causes this to happen? This is due to a phenomena known as

Dispersion of Light

The breaking of white light into its constituent spectrum of colours when it travels through a glass prism is known as dispersion of light (i.e. violet, indigo, blue, green, yellow, orange and red). Dispersion denotes 'distribution' in the figurative sense, and that is exactly what is happening in the image above. At varying frequencies and angles, white light breaks into its constituent hues.

Prism

A prism is a transparent refracting device with five plane surfaces that are tilted at different angles. The light is bent twice, with the emergent ray at an angle to the incident beam.

Angle of Deviation

The angle between the emerging and incident rays is known as the angle of deviation (δ).
In the case of a single refracting surface, δ = |i-r|
In case of a prism, δ=(i₁+ i₂)−(r1+r2) ]
δ = i₁+ i₂−A
Where,
A = Angle of prism.
For angle of minimum deviation, δ is minimum and i₁ = i₂= i
δmin=2i−A
For small A , δ=(μ−1)A

Prism Dispersion of White Light

The bending of the path of light as it moves from one medium to another is known as refraction. The degree to which light refracts is determined by the wavelength of the light. Because each light wave has a different wavelength, it will deviate in different ways. White light is made up of several wavelengths (colours) of light, such as violet, indigo, blue, green, yellow, and red. The maximum wavelength is red, while the lowest is violet.

The variation in the path of light is inversely proportional to the wavelength. The least deviated light is red, whereas the most deviated light is violet. When white light passes through a prism, a spectrum of seven hues appears, indicating that white light is made up of seven different colours.

Prism just serves as a conduit for the dispersion of light in the seven primary hues. When light strikes the prism, refraction occurs. These deviated colours have distinct wavelengths and frequencies, and they deviate differently at different angles due to the prism's velocity differential. As a result, the colour red deviates the least because it has the longest wavelength, while the colour violet deviates the most since it has the shortest wavelength.

Light Refraction via a Glass Prism

Three rectangular lateral surfaces and two triangular bases, all inclined at an angle, make up a glass prism. The 'Angle of the Prism' is the name given to this angle. Consider a triangular prism that has a ray of light passing through it.

Snell’s Law

According to Snell's law, light bends towards the normal when travelling from a rarer medium to a denser medium, and away from the normal when travelling from a denser medium to a rarer medium. Because glass is denser than air, when a light ray strikes the prism's surface, it bends towards the normal.

Light Dispersion and Rainbow

When it rains and the sun shines at the same time, a rainbow appears. When compared to a glass prism, each raindrop is composed of a different shape and has a different substance, but it still impacts light in the same way. When white light (sunlight) strikes a group of raindrops at a low angle, the seven constituent hues (red, orange, yellow, green, blue, indigo, and violet) can be seen.

The constituent hues of light slow down to varied speeds and frequencies as white sunshine travels from air into a drop of water. The raindrop bends at a steep angle as violet light enters it. Some of the light is reflected back, while the remainder is ejected into the air. Some of the reflected light escapes the drop, bending as it re-enters the atmosphere.

Each raindrop disperses the white sunshine into its component hues in this manner. Because we only see one colour from each raindrop, we see wide bands of colour, as if separate wet places were disseminating a different single hue. A double rainbow, consisting of a bright rainbow with a fainter rainbow above it, can also be seen on rare occasions.

The fainter rainbow appears in the same way as the sharper rainbow, except the light is reflected twice instead of once inside the raindrop. The light departs the raindrop at different angles as a result of the twofold reflection, and we see it above the sharper rainbow. You'll also note that the colours in the secondary rainbow are in the opposite sequence as the primary rainbow if you look closely.