On a rainy day, a rainbow is observed in the sky. Which optical phenomenon is primarily responsible for the formation of the different colours in a rainbow?

Introduction / Context:
Rainbows are among the most striking natural displays of optics. They appear as multicoloured arcs in the sky when sunlight interacts with water droplets in the atmosphere. While several optical processes are involved, one key phenomenon is responsible for splitting white sunlight into its colours and arranging them in order across the arc. This question asks you to identify that primary phenomenon.

Given Data / Assumptions:

• Sunlight is essentially white light, containing a spectrum of wavelengths.
• Raindrops in the atmosphere act as tiny transparent prisms or lenses.
• Light enters, travels through and may reflect internally in each raindrop.
• The observer sees an arc of colours from red to violet.

Concept / Approach:
White light is a mixture of different wavelengths. When it passes from one medium to another, such as from air into water, different wavelengths refract by slightly different amounts because the refractive index of the medium depends on wavelength. This separation of colours due to wavelength dependent refraction is called dispersion. In a rainbow, dispersion of sunlight by raindrops, combined with refraction and internal reflection, spreads the colours out into a continuous spectrum. Diffraction and thin film interference create other colourful patterns but are not the main mechanism of a rainbow.

Step-by-Step Solution:
Step 1: Recognise that sunlight entering a raindrop is refracted at the air water boundary. Step 2: Different wavelengths of light experience slightly different refractive indices in water. Step 3: Because of this, red, green and violet rays bend by different angles as they enter and exit the drop. Step 4: This separation of white light into its constituent colours is called dispersion. Step 5: Internal reflection inside the drop sends the dispersed rays back toward the observer. Step 6: The observer perceives an arc of colours, with red on the outside and violet on the inside, due primarily to dispersion.

Verification / Alternative check:
Prism experiments in school demonstrate dispersion clearly: when a narrow beam of white light passes through a glass prism, it spreads into a spectrum of colours. The behaviour of water droplets is similar in principle. Detailed ray tracing of light through a spherical drop shows that dispersion is necessary to separate colours into distinct angles, while refraction and reflection alone, without wavelength dependence, would not produce a colourful spectrum.

Why Other Options Are Wrong:
Diffraction of sunlight by raindrops: Diffraction effects occur when light encounters edges or apertures comparable to its wavelength, but they do not primarily create the ordered colour bands of a rainbow.

Interference in thin films: This phenomenon creates colour patterns in soap bubbles or oil films, where multiple reflections interfere, but it is not the main cause of a large scale rainbow in the sky.

Simple reflection from raindrops: Reflection alone would produce bright spots or glints but would not separate white light into a full spectrum of distinct colours.

Common Pitfalls:
Learners sometimes lump many optical phenomena together under the general idea of bending or spreading of light and mistakenly pick diffraction or interference. To avoid confusion, remember the classic association: prism plus white light gives a spectrum via dispersion. Rainbows are natural, large scale versions of the prism experiment, so dispersion is the key term to choose.

Final Answer:
The primary optical phenomenon responsible for a rainbow is dispersion of sunlight into its component colours.