Dispersion and Rainbow

Dispersion is the phenomenon where a beam of composite white light splits into its constituent component colors when passing through a refracting medium. This occurs because different colors of light travel at different speeds through a material medium, even though they all travel at the exact same speed (c = 3 × 10⁸ m/s) in a vacuum.

The Discovery by Sir Isaac Newton

In 1665, Sir Isaac Newton demonstrated that white light is not a single entity but a mixture of seven distinct visible colors. By passing sunlight through a glass prism, he projected the multi-colored band onto a screen. He confirmed that the prism does not create the colors but merely separates them by passing the split light through a second, inverted prism, which recombined the colors back into pure white light.

Cause of Dispersion

The underlying physical cause of dispersion lies in the varying refractive index of a medium for different wavelengths of light. This relationship is mathematically explained by Cauchy’s Formula:

Where A, B, and C are material-specific constants, and λ is the wavelength of light.

• Inverse Relationship: The refractive index (n) is inversely proportional to the wavelength (λ).
• Violet Light: Has the shortest wavelength in the visible spectrum. Consequently, it experiences the highest refractive index, travels the slowest in glass, and suffers the maximum deviation (bends the most).
• Red Light: Has the longest wavelength in the visible spectrum. Consequently, it experiences the lowest refractive index, travels the fastest in glass, and suffers the minimum deviation (bends the least).

The Visible Spectrum (VIBGYOR)

When white light undergoes dispersion, it forms a continuous band of colors called a spectrum. The colors are arranged in increasing order of wavelength and decreasing order of deviation, remembered by the acronym VIBGYOR.

Color	Approximate Wavelength (λ)	Speed in Medium	Degree of Deviation
Violet	∼ 400 nm	Slowest	Maximum
Indigo	∼ 425 nm	Very Slow	Very High
Blue	∼ 470 nm	Slow	High
Green	∼ 550 nm	Intermediate	Intermediate
Yellow	∼ 600 nm	Fast	Low
Orange	∼ 640 nm	Very Fast	Very Low
Red	∼ 700 nm	Fastest	Minimum

The Physics of a Rainbow

A rainbow is a natural optical spectrum produced by the dispersion of sunlight by tiny water droplets suspended in the atmosphere after rain. These ambient water droplets act as millions of miniature glass prisms.

Necessary Atmospheric Conditions

For an observer to view a rainbow, two conditions must be satisfied:

• The sun must be shining in one part of the sky (typically behind the observer).
• It must be raining or have recently rained in the opposite part of the sky (in front of the observer).
• The center of the rainbow’s arc is always diametrically opposite to the sun relative to the observer’s eye.

Step-by-Step Optical Mechanics inside a Raindrop

A single ray of sunlight undergoes three distinct optical phenomena sequentially when interacting with a spherical raindrop to form a primary rainbow:

1. Refraction and Dispersion: As sunlight enters the raindrop from the air, it slows down and bends. Because it is entering a denser medium, it simultaneously disperses into its seven component colors.
2. Total Internal Reflection (TIR): The dispersed light rays travel through the drop and strike the back inner wall of the water droplet. If the angle of incidence at this back interface is greater than the critical angle of water (≈ 48.75^°), the rays do not escape but reflect internally back through the droplet.
3. Refraction: The internally reflected rays travel back to the front surface and exit the droplet into the air, bending away from the normal and further intensifying the separation of colors before reaching the observer’s eye.

Primary vs. Secondary Rainbows

Often, two distinct rainbow arcs can be observed simultaneously in the sky. The brighter, lower arc is the Primary Rainbow, while the fainter, higher arc is the Secondary Rainbow.

Primary Rainbow

• Optical Process: Formed by two refractions (entry and exit) and one internal reflection inside the water droplet.
• Angular Dimensions: The red light emerges at an angle of 42^° and the violet light emerges at an angle of 40^° relative to the observer’s line of sight.
• Color Orientation: The outer edge of the arc is Red and the inner edge is Violet.
• Intensity: High visual brightness.

Secondary Rainbow

• Optical Process: Formed when sunlight strikes the bottom of the raindrop and undergoes two refractions and two successive internal reflections inside the droplet.
• Angular Dimensions: The colors emerge at a higher angle, with violet at 54^° and red at 51^° relative to the observer.
• Color Orientation: The color sequence is completely flipped due to the double reflection. The outer edge of the arc is Violet and the inner edge is Red.
• Intensity: Much fainter because light energy is lost with each subsequent internal reflection.

Feature	Primary Rainbow	Secondary Rainbow
Number of Internal Reflections	1	2
Angular Width / Position	40° to 42°	51° to 54°
Top/Outer Color	Red	Violet
Bottom/Inner Color	Violet	Red
Brightness Level	Vivid / Sharp	Faint / Dim

Key Trivia for Civil Services Examination

• Alexander’s Dark Band: This is the relatively dark region of the sky lying between the primary and secondary rainbows. It is named after the ancient Greek philosopher Alexander of Aphrodisias, who first described it in 200 AD. It occurs because the region between 42^° and 51^° cannot scatter light into the observer’s eye from either types of droplet reflections.
• The Full Circle Phenomenon: A rainbow is actually a complete, perfect circle. Observers on the ground only see a semi-circular arc because the lower half of the circle is cut off by the horizon line of the Earth. Pilots flying at high altitudes or passengers in airplanes can frequently see full-circle rainbows.
• No Two People See the Exact Same Rainbow: A rainbow does not exist at a fixed physical location in space. It is a purely optical pattern dependent on the position of the observer and the specific droplets scattering light into that observer’s eyes. As you move, your rainbow moves with you because you are receiving light from an entirely new set of raindrops.

Last Modified: May 28, 2026