When a ray of light is going from one medium to another, its :

1. Nature of Light and Electromagnetic Waves (basic)

To understand optics, we must first understand the mysterious nature of light itself. For centuries, scientists debated whether light was a stream of particles (corpuscles) or a wave. Today, we use Modern Quantum Theory to reconcile these views: light exhibits a dual nature, behaving as a wave in phenomena like diffraction and as a particle (photons) when interacting with matter Science, class X (NCERT 2025 ed.), Light – Reflection and Refraction, p.134. As an electromagnetic wave, light is unique because it does not require a material medium to travel—it can move through the vacuum of space at a staggering speed of approximately 3 × 10⁸ m/s.

When light travels through different materials (like air, water, or glass), its behavior is governed by the wave equation: v = fλ, where v is the speed, f is the frequency, and λ (lambda) is the wavelength. A critical rule to remember for your exams is that frequency (f) is an intrinsic property determined solely by the source of the light. Think of frequency as the "color identity" assigned at birth by the light bulb or the sun. Because it is tied to the vibration of the source, frequency does not change when light moves from one medium to another.

However, light does slow down when it enters a "denser" medium like glass. Since the frequency (f) must stay the same, the wavelength (λ) must decrease proportionally to compensate for the drop in speed (v) Science, class X (NCERT 2025 ed.), Light – Reflection and Refraction, p.148. This change in speed is the fundamental reason behind refraction, or the bending of light, which we will explore in the coming hops.

Property	When moving from Air to Glass...	Reasoning
Speed (v)	Decreases	Glass is optically denser than air.
Frequency (f)	Remains Constant	Determined only by the source.
Wavelength (λ)	Decreases	Must drop to satisfy v = fλ.

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

2. Refraction of Light and Snell's Law (basic)

When we observe a straw appearing bent in a glass of water, we are witnessing refraction. At its simplest, refraction is the change in the direction of light as it passes obliquely from one transparent medium to another. This occurs because light travels at different speeds in different materials. For instance, light travels fastest in a vacuum (approximately 3 × 10⁸ m/s) and slows down when it enters denser media like water or glass Science, class X (NCERT 2025 ed.), Chapter 9, p. 147.

To understand this deeply, we must look at light as a wave. The speed of light (v) is the product of its frequency (f) and its wavelength (λ), expressed as v = fλ. When light moves between media, its frequency remains constant because it is an intrinsic property determined by the source. Consequently, to account for the change in speed (v), the wavelength (λ) must change. When light enters an optically denser medium, both its speed and wavelength decrease, causing the ray to bend toward the normal.

The behavior of this bending is governed by two primary Laws of Refraction Science, class X (NCERT 2025 ed.), Chapter 9, p. 148:

• The Plane Law: The incident ray, the refracted ray, and the normal at the point of incidence all lie in the same plane.
• Snell’s Law: 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. Mathematically, sin i / sin r = constant. This constant is known as the refractive index of the second medium relative to the first.

Scenario	Bending Direction	Speed Change
Rarer to Denser (e.g., Air to Glass)	Towards the Normal	Decreases
Denser to Rarer (e.g., Water to Air)	Away from the Normal	Increases

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

3. Refractive Index and Speed of Propagation (intermediate)

When we talk about refraction, we are essentially talking about a change in the speed of light. In a vacuum, light travels at its cosmic speed limit of approximately 3 × 10⁸ m s⁻¹. However, as light enters a transparent medium like water or glass, it interacts with the atoms of that material, which causes it to slow down. The Refractive Index (n) is simply a numerical representation of this change. It is defined as the ratio of the speed of light in a vacuum (c) to the speed of light in the medium (v). This is expressed as n = c/v Science, Class X (NCERT 2025 ed.), Chapter 9: Light – Reflection and Refraction, p. 149.

To understand how this affects the nature of the light wave, we look at the wave equation: v = fλ (where v is speed, f is frequency, and λ is wavelength). A critical concept for the UPSC aspirant to master is that frequency is an intrinsic property of the light source. Think of it as the "heartbeat" of the light ray; once the source starts oscillating at a certain rate, that rate does not change as the light moves from one medium to another. Therefore, when light enters a denser medium (like moving from air to glass) and its speed (v) decreases, the wavelength (λ) must also decrease proportionally to keep the frequency constant.

Property	Change (Air → Glass)	Reasoning
Speed (v)	Decreases	Glass has a higher refractive index (n ≈ 1.50) than air (n ≈ 1.0003).
Frequency (f)	Remains Constant	Determined solely by the light source.
Wavelength (λ)	Decreases	Must decrease to compensate for the drop in speed (v = fλ).

It is also important to distinguish between mass density and optical density. A material like kerosene has a higher refractive index (1.44) than water (1.33), meaning light travels slower in kerosene, even though kerosene is physically less dense and floats on water Science, Class X (NCERT 2025 ed.), Chapter 9: Light – Reflection and Refraction, p. 149. In the context of refraction, "denser" always refers to optical density, which is a measure of a medium's ability to refract light.

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

4. Total Internal Reflection (TIR) (exam-level)

To understand Total Internal Reflection (TIR), we must first look at how light behaves when it tries to escape a 'denser' medium (like water or glass) into a 'rarer' medium (like air). When light travels from a denser to a rarer medium, it speeds up and bends away from the normal. As you increase the angle of incidence, the refracted ray leans further and further away from the normal line until it eventually lies flat along the boundary between the two media. The specific angle of incidence that causes the refracted ray to emerge at exactly 90° is known as the Critical Angle. Science, Class X (NCERT 2025 ed.), Chapter 9, p.148.

If you increase the angle of incidence even slightly beyond this critical angle, a fascinating shift occurs: the light can no longer escape into the second medium at all. Instead, it is entirely reflected back into the original denser medium. This is not just ordinary reflection; while a standard mirror absorbs some light, TIR is essentially 100% efficient, which is why it is called 'Total'. For this to happen, two strict conditions must be met: 1) Light must be traveling from an optically denser medium to an optically rarer medium, and 2) The angle of incidence must be greater than the critical angle for that pair of media. Science, Class X (NCERT 2025 ed.), Chapter 9, p.135.

This principle is the 'magic' behind several phenomena you see in the real world and in technology. For instance, Optical Fibers use TIR to carry internet data across oceans by trapping light inside thin glass strands. Similarly, the brilliance of a diamond is due to its very high refractive index (2.42), which results in a very small critical angle of about 24.4°. Science, Class X (NCERT 2025 ed.), Chapter 9, p.149. This small angle ensures that light entering the diamond is likely to undergo multiple internal reflections before exiting, creating that signature sparkle. In nature, TIR is also responsible for mirages seen on hot roads, where light from the sky reflects off the warm, less dense air near the ground.

Sources: Science, Class X (NCERT 2025 ed.), Light – Reflection and Refraction, p.148; Science, Class X (NCERT 2025 ed.), Light – Reflection and Refraction, p.135; Science, Class X (NCERT 2025 ed.), Light – Reflection and Refraction, p.149

5. Dispersion and Scattering of Light (intermediate)

To understand why the world is so colorful, we must look at how light behaves when it encounters different materials. While we often see 'white' sunlight, it is actually a mixture of seven colors. Dispersion is the phenomenon where white light splits into its component colors—Violet, Indigo, Blue, Green, Yellow, Orange, and Red (VIBGYOR)—when passing through a transparent medium like a glass prism Science, The Human Eye and the Colourful World, p.167. This happens because each color has a different wavelength. In a vacuum, all colors travel at the same speed, but in a medium like glass, shorter wavelengths (Violet) travel slower and bend more, while longer wavelengths (Red) travel faster and bend less Science, The Human Eye and the Colourful World, p.167. Unlike a rectangular glass slab where light emerges parallel to the incident ray, a prism's inclined surfaces cause the colors to emerge at different angles, creating a distinct spectrum Science, The Human Eye and the Colourful World, p.165.

While dispersion is about 'splitting' light, Scattering is about 'spreading' it. When light hits tiny particles in the atmosphere (like nitrogen or oxygen molecules), it is redirected in various directions. This is known as Rayleigh Scattering. The efficiency of scattering is inversely proportional to the fourth power of the wavelength. Consequently, shorter wavelengths (Blue/Violet) are scattered much more strongly than longer wavelengths (Red). This is why the sky appears blue during the day, but at sunrise or sunset—when light travels through a thicker layer of the atmosphere—only the least-scattered long wavelengths (Red) reach our eyes.

Feature	Red Light	Violet Light
Wavelength	Longest	Shortest
Speed in Glass	Higher	Lower
Angle of Deviation	Least Bending	Most Bending
Scattering in Atmosphere	Least Scattered	Most Scattered

Sources: Science, The Human Eye and the Colourful World, p.165; Science, The Human Eye and the Colourful World, p.167

6. The Wave Equation: Velocity, Wavelength, and Frequency (exam-level)

To understand how light behaves when it moves from one medium to another, we must first look at its nature as a wave. Every wave is defined by three fundamental properties: Velocity (v), which is the speed of propagation; Wavelength (λ), the horizontal distance between two successive crests; and Frequency (f), the number of waves passing a point in one second Physical Geography by PMF IAS, Tsunami, p.192. These three are bound together by the Wave Equation: v = fλ. In simple terms, the speed of a wave is the product of how "long" each wave is and how many of them pass by every second.

When light undergoes refraction, it transitions between materials of different optical densities, such as moving from air into a glass slab. This transition causes a change in the speed of the light ray Science, Class X (NCERT 2025 ed.), Light – Reflection and Refraction, p.148. Now, looking at our equation (v = fλ), if the velocity (v) changes, mathematically, either the frequency (f) or the wavelength (λ) must also change to keep the equation balanced. However, nature has a very specific rule here: Frequency is an intrinsic property of the source. Just as the pitch of a sound is determined by the vibrating string, the frequency of light is determined by the oscillation of the electrons at the source. It does not change when the wave enters a new medium.

Because frequency (f) remains constant, the wavelength (λ) must adjust proportionally to the change in velocity. If light enters a denser medium like glass, its velocity decreases. To maintain the equality, the wavelength must also decrease (the waves become "compressed"). Conversely, when light enters a rarer medium and speeds up, the wavelength increases. This is why we say that in refraction, velocity and wavelength are directly proportional, while frequency acts as the unwavering anchor of the wave.

Property	Change during Refraction (Rarer to Denser)	Reasoning
Velocity (v)	Decreases	Optical density of the medium slows the light down.
Frequency (f)	Remains Constant	Determined solely by the light source.
Wavelength (λ)	Decreases	Must decrease to satisfy the equation v = fλ.

Sources: Physical Geography by PMF IAS, Tsunami, p.192; Science, Class X (NCERT 2025 ed.), Light – Reflection and Refraction, p.148

7. Solving the Original PYQ (exam-level)

You have just mastered the fundamental building blocks of refraction and the wave equation ($v = f\lambda$). This PYQ is the perfect application of those concepts, testing your understanding of what happens at the boundary of two media. While you know that light changes its speed and direction when moving between materials of different optical densities, this question asks you to identify the one property that acts as an invariant anchor. By connecting your knowledge of electromagnetic waves, you can recall that frequency is determined solely by the source of the light and does not depend on the medium through which the light travels.

As a coach, I want you to visualize the logic: when a ray enters a denser medium (like glass from air), its speed decreases. According to the wave equation, if speed ($v$) drops, something else must change to keep the equation balanced. Since the frequency ($f$) is a fixed "identity" of the light source, the wavelength ($\lambda$) is forced to decrease proportionally. This fundamental rule is highlighted in Science, class X (NCERT 2025 ed.), which confirms that during refraction, the frequency remains same while speed and wavelength adjust based on the refractive index of the medium.

UPSC frequently uses options like wavelength remains same or frequency increases as traps to catch students who confuse these properties. Remember, wavelength is highly "flexible"—it stretches or shrinks depending on the medium's density. Options (C) and (D) are incorrect because they suggest a change in frequency or a specific direction of wavelength change that doesn't account for the nature of the media involved. By process of elimination and solid conceptual grounding, you can confidently identify that (B) frequency remains same is the only correct choice, as frequency is a source-dependent property rather than a medium-dependent one.