The spread in colours in a rainbow on sky is primarily due to

1. Refraction and Refractive Index (basic)

Welcome to your first step in mastering Geometrical Optics. To understand how light behaves, we must first understand Refraction. In simple terms, refraction is the change in the direction of light as it passes from one transparent medium to another. Think of it like a car driving from a smooth paved road onto a sandy beach at an angle; the wheels hitting the sand first will slow down, causing the car to swerve. Similarly, light bends because its speed changes depending on the medium it travels through Science, Class X (NCERT 2025 ed.), Light – Reflection and Refraction, p.159.

This phenomenon follows two fundamental Laws of Refraction. First, the incident ray, the refracted ray, and the 'normal' (an imaginary perpendicular line at the point of entry) all lie in the same plane. Second, and most importantly for our calculations, is Snell’s Law. It states that the ratio of the sine of the angle of incidence (i) to the sine of the angle of refraction (r) is a constant for a given pair of media. This constant is what we call the Refractive Index (n) Science, Class X (NCERT 2025 ed.), Light – Reflection and Refraction, p.148. Mathematically, it is expressed as:
n = sin i / sin r

The Absolute Refractive Index of a medium is specifically the ratio of the speed of light in a vacuum (c) to its speed in that medium (v), represented as nₘ = c / v. A higher refractive index means light travels slower in that medium, making it optically denser. It is vital to note that optical density is distinct from mass density; for instance, kerosene has a higher refractive index than water (meaning it is optically denser), even though it is physically lighter and floats on water Science, Class X (NCERT 2025 ed.), Light – Reflection and Refraction, p.149.

Medium Type	Speed of Light	Bending Behavior (from Air)
Optically Rarer (e.g., Air)	Faster	Baseline
Optically Denser (e.g., Glass)	Slower	Bends towards the normal

Sources: Science, Class X (NCERT 2025 ed.), Light – Reflection and Refraction, p.148; Science, Class X (NCERT 2025 ed.), Light – Reflection and Refraction, p.149; Science, Class X (NCERT 2025 ed.), Light – Reflection and Refraction, p.159

2. Total Internal Reflection (TIR) (intermediate)

To understand Total Internal Reflection (TIR), we must first look at how light behaves when it tries to change its 'neighborhood.' When light travels from an optically denser medium (like water or glass) to an optically rarer medium (like air), it bends away from the normal. As we increase the angle at which the light hits the boundary (the angle of incidence), the refracted ray bends further and further away until it eventually skims the surface.

There are two absolute 'must-have' conditions for TIR to occur:

• Direction: Light must be traveling from a denser medium to a rarer medium (e.g., from glass to air).
• The Critical Angle: The angle of incidence must be greater than the critical angle (the specific angle where the refracted ray would be 90°).

When the angle of incidence exceeds this critical threshold, the light cannot escape into the second medium at all. Instead, it is reflected back entirely into the original dense medium, obeying the standard laws of reflection (Science, Class X (NCERT 2025 ed.), Light – Reflection and Refraction, p.135). Unlike a silvered mirror, which absorbs a small portion of light, TIR reflects almost 100% of the energy, making it incredibly efficient for technology like optical fibers and explaining the brilliance of diamonds.

Feature	Refraction	Total Internal Reflection (TIR)
Medium Path	Denser to Rarer (or vice versa)	Only Denser to Rarer
Angle	Any angle (except 0°)	Incidence > Critical Angle
Light Energy	Transmitted into new medium	100% reflected back into original

Sources: Science, Class X (NCERT 2025 ed.), Light – Reflection and Refraction, p.135

3. Atmospheric Refraction (intermediate)

To understand Atmospheric Refraction, we must first look at the Earth's atmosphere not as a single block of air, but as a series of layers with varying densities. As we move from space toward the Earth's surface, the air becomes progressively denser. In optical terms, this means the refractive index of the air increases as we get closer to the ground. When light from a celestial body (like a star or the sun) enters this "graded medium," it doesn't travel in a straight line; instead, it continuously bends toward the normal (the vertical) because it is moving from a rarer medium to a denser one Science, Class X (NCERT 2025 ed.), Chapter 10, p.168.

This bending has a profound effect on where we perceive objects to be. Because our brains assume light travels in a perfectly straight line, we trace the light backward from the angle it enters our eyes. This results in the apparent position of a star being slightly higher in the sky than its actual position. This effect is most pronounced when objects are near the horizon, where the light must travel through the thickest portion of the atmosphere at a slant Physical Geography by PMF IAS, The Motions of The Earth and Their Effects, p.255.

Atmospheric refraction is also responsible for the twinkling of stars. Unlike planets, which appear as discs because they are closer, stars are "point sources" of light. As the physical conditions of the atmosphere—like temperature and air current—fluctuate, the path of the starlight shifts slightly. This causes the apparent position and the amount of light entering our eye to flicker, creating the twinkling effect Science, Class X (NCERT 2025 ed.), Chapter 10, p.168. Furthermore, this phenomenon gifts us extra daylight; we see the sun about 2 minutes before it actually crosses the horizon at sunrise and 2 minutes after it has set, effectively lengthening our day by about 4 minutes Science, Class X (NCERT 2025 ed.), Chapter 10, p.168.

Phenomenon	Impact of Refraction
Star Position	Appears higher than the actual geometric position.
Day Duration	Increased by ~4 minutes (2 mins at sunrise + 2 mins at sunset).
Sun's Shape	Appears flattened at sunrise/sunset due to differential refraction.

Sources: Science, Class X (NCERT 2025 ed.), Chapter 10: The Human Eye and the Colourful World, p.168; Physical Geography by PMF IAS, The Motions of The Earth and Their Effects, p.255

4. Scattering of Light and Tyndall Effect (intermediate)

Welcome back! In our previous sessions, we explored how light bends and reflects. Now, let’s look at what happens when light interacts with tiny particles in its path—a phenomenon called Scattering of Light. Unlike reflection from a large mirror, scattering occurs when light hits particles so small that they redirect the light in all directions. This interaction is the reason nature is so colorful!

The most famous demonstration of this is the Tyndall Effect. When a beam of light passes through a colloidal solution (like milk in water or smoke in a room), the path of the light becomes visible. This is because the particles are just the right size to scatter the light toward our eyes. In a true solution (like salt water), the particles are too small to scatter light, so the beam remains invisible Science, Class X, The Human Eye and the Colourful World, p.169.

In our atmosphere, scattering is a game of particle size vs. wavelength. The air is filled with molecules (nitrogen and oxygen) and aerosols (dust and soot). If the particle is much smaller than the wavelength of light, it scatters shorter wavelengths (blue) much more effectively than longer wavelengths (red). Specifically, blue light is scattered about 1.8 times more than red light Science, Class X, The Human Eye and the Colourful World, p.169. This is why the sky appears blue! However, if the particles are large—like the water droplets in a cloud—they scatter all colors of light almost equally, making the cloud appear white Physical Geography by PMF IAS, Horizontal Distribution of Temperature, p.283.

Particle Type	Size Relative to Wavelength	Resulting Phenomenon
Fine air molecules	Smaller than wavelength	Blue Sky (Selective scattering)
Dust/Water droplets	Larger than wavelength	White Clouds (Non-selective scattering)
Colloidal particles	Intermediate	Tyndall Effect (Visible beam)

This also explains the reddening of the sun at sunrise and sunset. At these times, sunlight travels through a much thicker layer of the atmosphere. Most of the blue light is scattered away long before it reaches you, leaving only the longer-wavelength red light to pass through and reach your eyes Science, Class X, The Human Eye and the Colourful World, p.169.

Sources: Science, Class X, The Human Eye and the Colourful World, p.169; Physical Geography by PMF IAS, Horizontal Distribution of Temperature, p.283

5. Dispersion of White Light (basic)

When we look at a beam of sunlight, it appears "white" or colorless. However, nature hides a vibrant secret within that beam. Dispersion is the phenomenon where white light splits into its constituent colors (the spectrum) when passing through a transparent medium like a glass prism or a raindrop. This happens because white light is actually a mixture of seven main colors, famously remembered by the acronym VIBGYOR (Violet, Indigo, Blue, Green, Yellow, Orange, and Red).

Why does this separation occur? It all comes down to the relationship between wavelength and bending. As light enters a denser medium (like glass) from a rarer medium (like air), it slows down and refracts. However, different colors of light have different wavelengths, and each wavelength travels at a slightly different speed within the glass. This causes them to bend through different angles with respect to the incident ray. Red light, having the longest wavelength, bends the least, while violet light, with the shortest wavelength, bends the most. Science, Class X (NCERT 2025 ed.), Chapter 10, p. 167

While a rectangular glass slab makes light emerge parallel to the entry ray, the triangular shape of a prism ensures that the refracted rays do not come back together, but instead fan out into a distinct band of colors. Science, Class X (NCERT 2025 ed.), Chapter 10, p. 165. This same principle is what creates a rainbow. In nature, tiny spherical water droplets act like miniature prisms. When sunlight enters a droplet, it is refracted and dispersed, then undergoes internal reflection at the back of the drop, and finally refracts again as it exits, sending a beautiful spectrum of light toward your eyes. Physical Geography by PMF IAS, Chapter 24, p. 335

Sources: Science, Class X (NCERT 2025 ed.), The Human Eye and the Colourful World, p.165-167; Physical Geography by PMF IAS, Hydrological Cycle, p.335

6. The Physics of Rainbow Formation (exam-level)

A rainbow is a magnificent natural spectrum that illustrates several fundamental principles of geometrical optics occurring simultaneously. To understand its formation, we must look at the interaction between sunlight and spherical water droplets suspended in the atmosphere. For an observer to see a rainbow, two conditions must be met: there must be moisture in the air (rain or mist) and the Sun must be behind the observer Science, The Human Eye and the Colourful World, p.167.

The process occurs in three distinct stages within a single water droplet:

• Refraction and Dispersion: As sunlight enters the water droplet, it moves from the less dense air into the denser water. This causes the light to bend (refract). However, because white light is composed of different wavelengths, each color bends at a slightly different angle—violet bends the most and red the least. This separation of white light into its constituent colors is known as dispersion. In this context, the droplet acts exactly like a tiny glass prism Science, The Human Eye and the Colourful World, p.167.
• Internal Reflection: The dispersed light travels to the back surface of the droplet. Here, it strikes the interface and undergoes internal reflection, bouncing back toward the front of the drop.
• Final Refraction: As the light exits the droplet, it refracts once more as it moves from water back into the air. This second refraction further enhances the separation of colors before they reach the observer's eye.

The sequence of these events ensures that different colors reach the observer at specific angles. For a primary rainbow, red light emerges at an angle of approximately 42° relative to the solar line, while violet emerges at about 40°. This angular precision is why a rainbow always appears as a circular arc; you are seeing the light from all droplets that sit at those specific angles relative to your eye.

Phenomenon	Role in Rainbow Formation
Refraction	Bends the light as it enters and exits the droplet.
Dispersion	Splits white sunlight into its component colors (VIBGYOR).
Internal Reflection	Redirects the light back toward the observer.

Sources: Science, The Human Eye and the Colourful World, p.167

7. Solving the Original PYQ (exam-level)

Now that you have mastered the individual building blocks of optics—refraction, reflection, and dispersion—you can see how they converge in this classic UPSC problem. The question asks for the primary reason for the "spread in colors," which is the crucial hint. While a rainbow is a complex atmospheric phenomenon involving a sequence of events, the specific act of white light splitting into its constituent VIBGYOR spectrum is defined as dispersion of sunlight. Your conceptual understanding of how different wavelengths of light bend at slightly different angles when entering a new medium is the key to unlocking this answer.

To arrive at the correct reasoning, imagine the journey of a single ray of sunlight. As it enters a spherical water droplet, it slows down and bends—this is refraction. However, because violet light bends more than red light, the white light immediately begins to fan out inside the drop; this is the dispersion phase. The light then hits the back of the droplet and undergoes internal reflection before refracting again as it exits. While all these steps are necessary to redirect the light back to your eye, the "spread" or separation itself is a direct result of the water droplet acting as a natural prism, as explained in Science, class X (NCERT 2025 ed.).

UPSC often includes the other options as distractors because they are indeed part of the process. Refraction and reflection are certainly occurring, but they do not inherently cause the separation of colors—a standard mirror reflects light without creating a rainbow. Total internal reflection is a common trap; however, in a primary rainbow, the light undergoes simple internal reflection, and even if it were total, it would only be responsible for the direction of the light, not the spectral separation. Therefore, dispersion of sunlight remains the most precise and fundamental cause of the colorful display you see in the sky.