Rainbow is produced when sunlight falls on drops of rain. Which of the following physical phenomena are responsible for this? 1. Dispersion 2. Refraction 3. Internal reflection Select the correct answer using the codes given below.

1. Basics of Refraction and Bending of Light (basic)

Welcome to our first step into the fascinating world of Geometrical Optics. To understand how light behaves, we must first appreciate its fundamental preference: it loves to travel in straight lines as long as the medium remains the same Science, Class X (NCERT 2025 ed.), Chapter 9, p.134. However, when light travels obliquely (at an angle) from one transparent medium to another—say, from the air into a glass of water—it undergoes a sudden change in direction at the boundary. This phenomenon is what we call Refraction.

Why does light bend? The secret lies in its speed. While light travels at a blistering speed of approximately 3 × 10⁸ m/s in a vacuum, it slows down significantly when it enters denser materials like water or glass Science, Class X (NCERT 2025 ed.), Chapter 9, p.148. This change in speed causes the wavefront to pivot, leading to a bend. We measure this "bending power" using the Refractive Index (n), which is simply the ratio of the speed of light in the first medium to the speed of light in the second medium (n₂₁ = v₁ / v₂).

Refraction isn't chaotic; it follows two strict Laws of Refraction Science, Class X (NCERT 2025 ed.), Chapter 9, p.148. First, the incident ray, the refracted ray, and the 'normal' (the imaginary line perpendicular to the surface) all sit in the same flat plane. Second, we have Snell’s Law, which tells us 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 specific pair of media. This constant is exactly what defines the refractive index of the second medium relative to the first.

Sources: Science, Class X (NCERT 2025 ed.), Chapter 9: Light – Reflection and Refraction, p.134; Science, Class X (NCERT 2025 ed.), Chapter 9: Light – Reflection and Refraction, p.148

2. Dispersion: Splitting White Light (basic)

When we look at a beam of sunlight, it appears colorless or "white." However, nature hides a vibrant secret within that beam. Dispersion is the phenomenon where white light splits into its constituent colors when passing through a transparent medium like a glass prism. This happens because "white light" is actually a mixture of seven different colors. While these colors travel at the same speed in a vacuum, they travel at different speeds when they enter a denser medium like glass or water. This difference in speed causes each color to bend (refract) by a different angle, effectively fanning them out into a beautiful band called a spectrum.

To understand why this happens, we look at the geometry of a triangular glass prism. Unlike a rectangular glass slab where the opposite faces are parallel, a prism has two triangular bases and three rectangular lateral surfaces that are inclined at an angle to each other Science, Class X (NCERT 2025 ed.), Chapter 10, p.165. When white light enters this inclined surface, Red light, which has the longest wavelength, travels the fastest in glass and deviates the least. Conversely, Violet light, with the shortest wavelength, travels the slowest and deviates the most Science, Class X (NCERT 2025 ed.), Chapter 10, p.167. This differential bending creates the distinct sequence we see on a screen.

A pivotal moment in science occurred when Sir Isaac Newton used a second, identical prism in an inverted position relative to the first. He observed that the colors separated by the first prism were recombined by the second prism to emerge as white light once again Science, Class X (NCERT 2025 ed.), Chapter 10, p.167. This brilliant experiment proved that the prism itself wasn't "coloring" the light; rather, it was simply separating the colors already present within sunlight. Today, we define any light that produces a spectrum similar to sunlight as white light.

Sources: Science, Class X (NCERT 2025 ed.), Chapter 10: The Human Eye and the Colourful World, p.165-167

3. Total Internal Reflection (TIR) and its Conditions (intermediate)

Welcome back! Now that we understand how light bends when crossing boundaries, let’s look at a fascinating "limit" to refraction called Total Internal Reflection (TIR). Imagine you are underwater, looking up at the surface. As you change your viewing angle, the surface eventually stops looking like a window to the sky and starts looking like a perfect silver mirror. This is TIR in action.

To understand why this happens, we must look at light moving from an optically denser medium (like water or glass) to an optically rarer medium (like air). According to Snell's Law Science, Chapter 9, p.148, as the light enters the rarer medium, it bends away from the normal. As we increase the angle of incidence (i), the angle of refraction (r) also increases until it reaches a limit. The specific angle of incidence that results in an angle of refraction of exactly 90° is called the Critical Angle.

If you increase the angle of incidence even a fraction beyond this critical angle, the light cannot refract into the second medium at all. Instead, it is reflected back into the original denser medium. In this state, the interface behaves like a 100% efficient mirror, following the standard laws of reflection where the angle of incidence equals the angle of reflection Science, Chapter 9, p.135. This is why we call it "total" — unlike a glass mirror which absorbs a small amount of light, TIR reflects almost all of it.

Refractive indices vary significantly between materials; for instance, water has an index of 1.33 while diamond has a much higher index of 2.42 Science, Chapter 9, p.149. This high refractive index is exactly why diamonds are so sparkly — they have a very small critical angle, making it easy for light to get trapped inside and undergo multiple internal reflections before exiting toward your eye.

Sources: Science, Chapter 9: Light – Reflection and Refraction, p.135; Science, Chapter 9: Light – Reflection and Refraction, p.148; Science, Chapter 9: Light – Reflection and Refraction, p.149

4. Scattering of Light and the Tyndall Effect (intermediate)

When we look at a clear blue sky or watch a beam of sunlight pierce through a dusty room, we are witnessing the scattering of light. In a vacuum, light travels in a perfectly straight line; however, when it encounters obstacles like molecules, dust, or water droplets, it gets deflected in various directions. This phenomenon where the path of light becomes visible due to interaction with particles is known as the Tyndall effect Science, Class X (NCERT 2025 ed.), Chapter 10, p.169.

The most critical factor in scattering is the size of the particle relative to the wavelength of the light. Generally, if the wavelength of the incoming radiation is greater than the radius of the obstructing particle (like a gas molecule), scattering occurs. Conversely, if the particle is much larger (like a heavy dust grain), the light may simply reflect off it Physical Geography by PMF IAS, Horizontal Distribution of Temperature, p.283. This relationship dictates exactly what color we see:

Interestingly, the atmosphere acts as a massive filter. If Earth had no atmosphere, there would be no particles to scatter the sunlight toward our eyes from different angles. In such a scenario, the sky would look completely dark, just as it appears to astronauts in space Science, Class X (NCERT 2025 ed.), Chapter 10, p.169. This highlights that the "color" of the sky is not a property of the air itself, but a result of how sunlight interacts with the particles within it.

Sources: Science, class X (NCERT 2025 ed.), Chapter 10: The Human Eye and the Colourful World, p.169; Physical Geography by PMF IAS, Horizontal Distribution of Temperature, p.283

5. Atmospheric Refraction Phenomena (intermediate)

When we look at the night sky or watch a sunset, we aren't seeing things exactly where they are. This is due to Atmospheric Refraction — the bending of light as it passes through the Earth's atmosphere. Because the atmosphere is not uniform, its density (and therefore its refractive index) increases as we get closer to the Earth's surface. Light coming from space enters thinner air first and gradually moves into denser layers, causing it to bend continuously towards the normal.

This phenomenon leads to several fascinating optical effects in our daily lives:

• Apparent Position of Stars: Since the atmosphere bends starlight towards the Earth, our eyes trace the light back in a straight line, making stars appear slightly higher in the sky than their actual position Science, Chapter 10, p.168.
• Twinkling of Stars: The atmosphere is not a static block of air; it is a turbulent medium with varying temperatures and densities. As these conditions change rapidly, the refractive index of the air through which the starlight passes fluctuates. This causes the apparent position and the amount of light entering our eye to flicker, which we perceive as twinkling Science, Chapter 10, p.168.
• Early Sunrise and Delayed Sunset: This is a classic UPSC favorite. Because of the bending of light, the Sun becomes visible to us about 2 minutes before it actually crosses the horizon in the morning, and remains visible for about 2 minutes after it has actually set in the evening Physical Geography by PMF IAS, The Motions of The Earth and Their Effects, p.255. This effectively increases the duration of daylight by approximately 4 minutes.

Another interesting detail is the flattening of the Sun’s disc at sunrise and sunset. This happens because the light from the bottom edge of the Sun travels through more atmosphere and is refracted more than the light from the top edge, creating an oval appearance Science, Chapter 10, p.168.

Sources: Science, The Human Eye and the Colourful World, p.168; Physical Geography by PMF IAS, The Motions of The Earth and Their Effects, p.255

6. Mechanics of Rainbow Formation (exam-level)

A rainbow is one of nature’s most beautiful optical displays, but from a physics perspective, it is a sophisticated "three-act play" involving light interacting with spherical water droplets. To understand its formation, we must look at what happens inside a single raindrop. The process is triggered by three distinct physical phenomena: refraction, dispersion, and internal reflection.

When sunlight strikes a raindrop, the first stage is refraction and dispersion. As light moves from the air into the denser medium of water, it slows down and bends (refracts). Because white light is composed of different wavelengths (colors), and each wavelength travels at a slightly different speed in water, the light splits into its constituent colors. This splitting is called dispersion, and it turns the raindrop into a tiny, natural prism Science, Class X (NCERT 2025 ed.), Chapter 10, p.167.

The second stage occurs at the back of the droplet. The dispersed light hits the inner surface and undergoes internal reflection, which sends the light back toward the front of the drop. It is a common misconception that this is always "Total Internal Reflection" (TIR); in reality, it is often a partial reflection where some light escapes out the back, but enough is reflected to reach our eyes. Finally, as the light exits the droplet, it refracts again, bending one last time as it moves from water back into the air. This final exit further spreads the colors into the distinct arc we recognize in the sky Science, Class X (NCERT 2025 ed.), Chapter 10, p.167.

For an observer to see a rainbow, specific geometric conditions must be met: the Sun must be behind the observer and the water droplets must be in front. This is why you can sometimes create a "mini-rainbow" using a garden hose or by looking at a waterfall with your back to the Sun.

Sources: Science, Class X (NCERT 2025 ed.), Chapter 10: The Human Eye and the Colourful World, p.167

7. Solving the Original PYQ (exam-level)

Now that you have mastered the individual properties of light, this classic UPSC question demonstrates how those building blocks integrate to create a complex natural phenomenon. The formation of a rainbow acts as a perfect synthesis of refraction, dispersion, and internal reflection. As sunlight enters a raindrop, the change in medium from air to water causes the light to bend—this is refraction. Simultaneously, because water has a different refractive index for different colors, the white light splits into its constituent spectrum, a process known as dispersion. This illustrates that a single raindrop effectively functions as a tiny, liquid prism.

To reach the observer's eye, the light must not pass straight through the droplet; instead, it must bounce off the back surface. This is where internal reflection occurs, redirecting the spectrum back toward the front of the drop. As noted in Science, Class X (NCERT), the light then undergoes a final stage of refraction as it exits the droplet into the air, further separating the colors. Because all three processes are mandatory to form the visible arc we see in the sky, the correct answer is (D) 1, 2 and 3.

UPSC frequently uses partial truths as traps. Options (A), (B), and (C) are incorrect because they fail to account for the complete optical path. For instance, without internal reflection, the light would simply exit the back of the raindrop, and no rainbow would be visible to an observer standing with their back to the sun. Furthermore, while some advanced physics texts debate whether this is "Total" Internal Reflection (TIR) or just partial internal reflection, the UPSC wisely uses the broader term internal reflection to encompass the essential bounce that directs the light toward your eyes. Always look for the option that captures the entirety of the physical mechanism described.