The speed of light will be minimum while passing through

1. Nature of Light and Electromagnetic Waves (basic)

2. Reflection and Spherical Mirrors (basic)

Welcome! Let’s start our journey into Geometrical Optics by looking at how light interacts with surfaces. When light hits a highly polished surface, such as a mirror, it doesn’t pass through; instead, it bounces back into the same medium. This phenomenon is called reflection. Whether the surface is flat (plane) or curved (spherical), the Laws of Reflection always hold true:

• The angle of incidence (∠i) is always equal to the angle of reflection (∠r).
• The incident ray, the reflected ray, and the normal (a perpendicular line to the surface) at the point of incidence all lie in the same plane.

As noted in Science, Class X (NCERT 2025 ed.), Chapter 9, p.134, these laws are fundamental and apply to all types of reflecting surfaces.

When we move beyond flat mirrors, we encounter spherical mirrors. Imagine a hollow glass sphere; if you cut a piece out and silver one side, you get a spherical mirror. We categorize them based on which way the reflecting surface curves:

As explained in Science, Class VIII, NCERT (Revised ed 2025), Light: Mirrors and Lenses, p.155, a simple side-view helps us distinguish these: a concave mirror looks like a "cave" you can enter, while a convex mirror curves away. These mirrors don't just reflect light; they change its path to form different types of images. A real image is formed when light rays actually meet at a point (and can be caught on a screen), while a virtual image occurs when rays only appear to diverge from a point behind the mirror.

Sources: Science, Class X (NCERT 2025 ed.), Chapter 9: Light – Reflection and Refraction, p.134; Science, Class VIII, NCERT (Revised ed 2025), Light: Mirrors and Lenses, p.155; Science, Class X (NCERT 2025 ed.), Chapter 9: Light – Reflection and Refraction, p.158

3. Total Internal Reflection (TIR) (intermediate)

To understand Total Internal Reflection (TIR), we must first look at how light behaves when it tries to speed up. When light travels from an optically denser medium (like glass or water) to an optically rarer medium (like air), it bends away from the normal. This happens because the speed of light increases as the refractive index (n) decreases, following the relation n = c/v Science, Class X, Chapter 9, p.149.

As we gradually increase the angle of incidence (i) in the denser medium, the refracted ray in the rarer medium bends further and further away from the normal. Eventually, we reach a specific point called the Critical Angle (C). At this precise angle, the refracted ray doesn't enter the second medium at all; instead, it skims along the interface, making an angle of refraction of 90° Science, Class X, Chapter 9, p.148. If you increase the incident angle even a fraction beyond this critical point, the light is "trapped" and reflects entirely back into the original denser medium. This is Total Internal Reflection.

For TIR to occur, two absolute conditions must be met: 1) Light must be moving from a denser to a rarer medium, and 2) The angle of incidence must exceed the critical angle. This phenomenon is why diamonds sparkle so intensely—their high refractive index (2.42) results in a very small critical angle, meaning light is easily trapped and reflected multiple times inside the stone before escaping Science, Class X, Chapter 9, p.149. It is also the fundamental principle behind optical fibers, which carry our internet data across the globe with almost zero signal loss.

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

4. Scattering and Dispersion of Light (intermediate)

Welcome to a beautiful intersection of physics and nature. When we look at a rainbow or the deep blue of the midday sky, we are witnessing two distinct phenomena: Dispersion and Scattering. While they both involve the interaction of light with matter, they happen for very different reasons.

Dispersion is the splitting of white light into its constituent colors (VIBGYOR). This happens because, although all colors of light travel at the same speed in a vacuum, they travel at different speeds in a medium like glass or water. When white light enters a triangular glass prism, the refractive index of the glass is slightly different for each color. Specifically, red light (longer wavelength) bends the least, while violet light (shorter wavelength) bends the most Science, Class X (NCERT 2025), Chapter 10, p.167. This differential bending is what spreads the light out into a spectrum.

Scattering, on the other hand, is the deflection of light in various directions by particles in the atmosphere. The molecules of air and fine dust are much smaller than the wavelength of visible light. These tiny particles are far more effective at scattering shorter wavelengths (the blue end) than longer wavelengths (the red end) Science, Class X (NCERT 2025), Chapter 10, p.169. This is why the sky appears blue—the atmosphere intercepts sunlight and scatters the blue light in every direction towards our eyes. During sunrise or sunset, light has to travel through a thicker layer of the atmosphere; most of the blue is scattered away before reaching us, leaving only the less-scattered red light to color the horizon Fundamentals of Physical Geography, Class XI (NCERT 2025), Chapter 8, p.68.

It is also fascinating to note that atmospheric dust isn't just for color. Many dust particles are hygroscopic, meaning they attract moisture. This makes them critical as "condensation nuclei" around which clouds and rain form Physical Geography by PMF IAS, Chapter: Earth's Atmosphere, p.273. Without these tiny suspended particles, we would have neither the blue sky nor the rain that sustains life.

Sources: Science, Class X (NCERT 2025), The Human Eye and the Colourful World, p.167, 169; Fundamentals of Physical Geography, Class XI (NCERT 2025), Solar Radiation, Heat Balance and Temperature, p.68; Physical Geography by PMF IAS, Earths Atmosphere, p.273

5. Refraction and Snell's Law (basic)

When light travels from one transparent medium to another, it rarely continues in a straight line; instead, it changes direction at the interface. This phenomenon is called refraction. The root cause of this bending is the change in the speed of light as it moves between media. While light travels at its maximum speed of approximately 3 × 10⁸ m/s in a vacuum, it slows down when entering substances like water or glass Science, Class X (NCERT 2025 ed.), Chapter 9, p.148.

To quantify how much a medium affects the speed of light, we use the Refractive Index (n). The absolute refractive index of a medium is the ratio of the speed of light in a vacuum (c) to the speed of light in that medium (v), expressed as n = c/v. Because the speed of light in any medium is always less than in a vacuum, the refractive index is always greater than 1. A higher refractive index indicates that light travels slower in that medium. We refer to media with a higher refractive index as optically denser, and those with a lower refractive index as optically rarer Science, Class X (NCERT 2025 ed.), Chapter 9, p.149.

The actual behavior of the light ray follows two fundamental Laws of Refraction. First, the incident ray, the refracted ray, and the normal at the point of incidence all lie in the same plane. Second, the Snell’s Law of Refraction 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: sin i / sin r = constant Science, Class X (NCERT 2025 ed.), Chapter 9, p.148. This constant is the refractive index of the second medium relative to the first.

How the light bends depends on the change in optical density. When light travels from a rarer to a denser medium (e.g., air to glass), it slows down and bends towards the normal. Conversely, when moving from a denser to a rarer medium (e.g., glass to air), it speeds up and bends away from the normal Science, Class X (NCERT 2025 ed.), Chapter 9, p.147.

Sources: Science, Class X (NCERT 2025 ed.), Chapter 9: Light – Reflection and Refraction, p.147; Science, Class X (NCERT 2025 ed.), Chapter 9: Light – Reflection and Refraction, p.148; Science, Class X (NCERT 2025 ed.), Chapter 9: Light – Reflection and Refraction, p.149

6. Refractive Index and Optical Density (exam-level)

When light travels from one medium to another, it doesn't just change direction; it changes speed. The Refractive Index (n) is the mathematical tool we use to quantify this change. At its simplest, it is a ratio: the speed of light in a vacuum (c) divided by the speed of light in the medium (v). Because the speed of light in a vacuum is the universal "speed limit" (approximately 300,000 km/s), the refractive index of any material is always greater than 1. As noted in Science, Class X (NCERT 2025 ed.), Chapter 9, p.149, the speed of light in air is only marginally less than in a vacuum, giving it a refractive index of 1.0003, whereas it reduces significantly in materials like glass or water.

We distinguish between Absolute Refractive Index (comparison with a vacuum) and Relative Refractive Index (comparison between any two media). For instance, if light moves from medium 1 to medium 2, the refractive index of medium 2 with respect to medium 1 (n₂₁) is the ratio of the speed of light in medium 1 to the speed in medium 2 (Science, Class X (NCERT 2025 ed.), Chapter 9, p.148). This leads to a crucial rule: The higher the refractive index, the slower light travels in that medium. This is why light moves slowest in Diamond (n = 2.42), which has the highest refractive index among common materials.

A common point of confusion in competitive exams is the difference between mass density and optical density. Optical density is specifically the ability of a medium to refract light; it is not the same as "heaviness" or mass per unit volume. A classic example is Kerosene: it has a higher refractive index (1.44) than water (1.33), meaning it is optically denser, even though kerosene is physically lighter than water and floats on it (Science, Class X (NCERT 2025 ed.), Chapter 9, p.149-150).

Sources: Science, Class X (NCERT 2025 ed.), Chapter 9: Light – Reflection and Refraction, p.148; Science, Class X (NCERT 2025 ed.), Chapter 9: Light – Reflection and Refraction, p.149; Science, Class X (NCERT 2025 ed.), Chapter 9: Light – Reflection and Refraction, p.150

7. Solving the Original PYQ (exam-level)

This question is a perfect application of the relationship between optical density and the refractive index that we just covered. You’ve learned that as light moves from one medium to another, its speed changes based on how much the medium resists its flow. According to the fundamental formula n = c/v, the refractive index (n) is inversely proportional to the velocity (v) of light in that medium. Therefore, to find where the speed is minimum, we simply need to identify the medium with the highest refractive index among the choices provided.

Walking through the data provided in Science, class X (NCERT 2025 ed.), we see a clear hierarchy of optical density: vacuum has the lowest possible index (1.00), followed closely by air (1.0003). Water follows with a significantly higher index of approximately 1.33, but glass typically has an index of 1.50 or higher. Since glass is the optically densest material on this list, it slows light down the most relative to its speed in a vacuum. This logical deduction leads us directly to (A) glass as the correct answer.

In a UPSC setting, the most common trap is the vacuum/air confusion; students often rush and pick vacuum because it is a "special" case, forgetting that it represents the maximum speed of light (3 × 10⁸ m/s), not the minimum. Another trap is failing to distinguish between water and glass; always remember that solids like glass are generally optically denser than liquids like water. Always read the question carefully to see if it asks for the maximum or minimum speed, as this one simple word changes the answer from vacuum to glass.