If a substance is behaving as convex lens in air and concave lens in water then which one of the following is its refractive index?

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

Welcome to your first step in mastering Geometrical Optics! To understand how lenses and mirrors work, we must first understand why light behaves the way it does when it moves between different materials. Imagine you are running on a paved road and then suddenly step into deep sand; you naturally slow down. Light does something very similar. When a ray of light travels from one medium (like air) into another (like glass or water), its speed changes, which causes it to bend. This phenomenon of light changing direction at the interface of two media is called Refraction Science, Chapter 9, p.147.

This bending isn't random; it follows two fundamental Laws of Refraction. First, the incident ray, the refracted ray, and the 'normal' (an imaginary line perpendicular to the surface) all lie in the same flat plane. Second, we have Snell’s Law, which gives us a mathematical way to predict the bend: 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 Science, Chapter 9, p.148. This constant is known as the Refractive Index (n). Formally, the Refractive Index of a medium is the ratio of the speed of light in a vacuum to its speed in that specific medium (n = c/v) Science, Chapter 9, p.159.

To visualize this, think of the Optical Density of the material. A medium with a higher refractive index is considered 'optically denser.' When light enters an optically denser medium (like moving from air to glass), it slows down and bends toward the normal. Conversely, when it exits into a rarer medium (like moving from glass back to air), it speeds up and bends away from the normal. This simple principle of 'bending' is the foundation of every camera lens, pair of spectacles, and telescope in existence!

Sources: Science, Light – Reflection and Refraction, p.147; Science, Light – Reflection and Refraction, p.148; Science, Light – Reflection and Refraction, p.159

2. Understanding Refractive Index (n) (basic)

To understand how light behaves when it moves from one material to another, we must first understand its "speed limit." While light travels at its maximum possible speed in a vacuum (approximately 3 × 10⁸ m/s), it slows down when it enters transparent materials like water or glass. The Refractive Index (n) is simply a numerical value that tells us how much a medium slows down light compared to its speed in a vacuum Science, Chapter 9, p.148. It is a dimensionless constant—a ratio—that acts as a signature for every transparent substance.

There are two ways to look at this value. The Absolute Refractive Index (usually just called the refractive index) compares the speed of light in a vacuum (c) to the speed of light in the medium (v). The formula is expressed as n = c/v Science, Chapter 9, p.149. Because light always travels slower in a medium than in a vacuum, this value is always greater than 1. For example, the refractive index of water is 1.33, while for a diamond, it is a much higher 2.42, meaning light travels significantly slower through a diamond Science, Chapter 9, p.149.

It is crucial to distinguish between mass density and optical density. In common parlance, "dense" often refers to how heavy something is (mass per unit volume). However, in optics, an "optically denser" medium is simply one with a higher refractive index, where light travels slower Science, Chapter 9, p.150. Interestingly, a substance can be more optically dense even if it is physically lighter. For instance, kerosene has a higher refractive index (1.44) than water (1.33), making it more optically dense, even though kerosene floats on water due to lower mass density Science, Chapter 9, p.149-150.

Sources: Science, Chapter 9: Light – Reflection and Refraction, p.148; Science, Chapter 9: Light – Reflection and Refraction, p.149; Science, Chapter 9: Light – Reflection and Refraction, p.150

3. Spherical Lenses: Converging and Diverging (basic)

A spherical lens is a piece of transparent material (like glass or plastic) bound by two surfaces, where at least one surface is spherical. Think of these as slices of a glass sphere. The most fundamental way to categorize these lenses is by how they interact with light: do they bring rays together (converge) or spread them apart (diverge)?

A Convex Lens (also called a double convex lens) is thicker in the middle than at its edges. When parallel rays of light pass through it, they bend inward and meet at a single point called the Principal Focus (F). Because of this property, we call it a converging lens Science, Class X (NCERT 2025 ed.), Chapter 9, p.150. In contrast, a Concave Lens is thinner in the middle and thicker at the edges. It causes parallel light rays to bend outward as if they are originating from a point behind the lens. This makes it a diverging lens Science, Class X (NCERT 2025 ed.), Chapter 9, p.150.

It is important to understand that the behavior of a lens isn't just about its shape—it is also about the medium it is in. Usually, we assume the lens is in air. A lens converges light if its refractive index is higher than the surrounding medium. If you were to place a glass convex lens in a liquid that is denser than glass, it would actually start behaving like a concave lens! This happens because the bending of light depends on the ratio (n_lens / n_medium). According to the sign convention, we measure all distances from the optical centre of the lens Science, Class X (NCERT 2025 ed.), Chapter 9, p.155.

Sources: Science, Class X (NCERT 2025 ed.), Chapter 9: Light – Reflection and Refraction, p.150; Science, Class X (NCERT 2025 ed.), Chapter 9: Light – Reflection and Refraction, p.151; Science, Class X (NCERT 2025 ed.), Chapter 9: Light – Reflection and Refraction, p.155

4. Total Internal Reflection and Critical Angle (intermediate)

Hello! Now that we have mastered the basics of how light bends through different materials, we come to a fascinating phenomenon where a transparent boundary suddenly starts acting like a perfect mirror. This is known as Total Internal Reflection (TIR). To understand this, we must look at what happens when light attempts to travel from an optically denser medium (like water or glass) to an optically rarer medium (like air).

According to Snell’s Law, light moving from a denser to a rarer medium bends away from the normal Science, Chapter 9, p.148. As we gradually increase the angle of incidence (i) in the denser medium, the angle of refraction (r) in the rarer medium also increases, bending closer and closer to the interface. Eventually, we reach a specific tipping point called the Critical Angle (θc). At this precise angle, the refracted ray doesn't enter the second medium at all; instead, it skims along the boundary, making an angle of refraction of exactly 90°.

If the angle of incidence is increased even a fraction beyond this critical angle, refraction becomes impossible. The boundary then reflects 100% of the light back into the original denser medium. This is Total Internal Reflection. Unlike a silvered mirror, which absorbs some light, TIR is a "total" process, making it incredibly efficient for technologies like optical fibers or explaining the extreme brilliance of a diamond, which has a very high refractive index of 2.42 Science, Chapter 9, p.149.

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

5. Dispersion and Scattering of Light (intermediate)

When we talk about the beauty of a rainbow or the deep blue of the sky, we are witnessing two fundamental behaviors of light: Dispersion and Scattering. While they both involve the "separation" of light, they happen for very different reasons. Let’s break them down from first principles.

1. Dispersion: The Prism Effect
When white light enters a transparent medium like a glass prism, it splits into its seven constituent colors (VIBGYOR). This happens because different colors of light travel at different speeds in a medium, even though they all travel at the same speed in a vacuum. Because they change speed by different amounts, they refract (bend) at different angles. Red light, having a longer wavelength, travels the fastest in glass and bends the least, while violet light travels the slowest and bends the most Science, Class X (NCERT 2025 ed.), The Human Eye and the Colourful World, p.167. This angular separation creates a spectrum.

2. Scattering: The Atmospheric Interaction
Scattering occurs when light hits tiny particles (like air molecules or dust) and is redirected in all directions. The efficiency of this redirection depends on the size of the particle relative to the wavelength of light. Small molecules in our atmosphere are much more effective at scattering shorter wavelengths (blue/violet) than longer wavelengths (red). This is why the sky appears blue; as sunlight travels through the atmosphere, the blue light is scattered in every direction, reaching our eyes from all parts of the sky Fundamentals of Physical Geography, Geography Class XI (NCERT 2025 ed.), Solar Radiation, Heat Balance and Temperature, p.68. If there were no atmosphere, the sky would look black Science, Class X (NCERT 2025 ed.), The Human Eye and the Colourful World, p.169.

Sources: Science, Class X (NCERT 2025 ed.), The Human Eye and the Colourful World, p.165-169; Fundamentals of Physical Geography, Geography Class XI (NCERT 2025 ed.), Solar Radiation, Heat Balance and Temperature, p.68

6. Effect of Surrounding Medium on Lens Behavior (exam-level)

When we think of a lens, we often assume its behavior is fixed—for instance, a convex lens is "always" a converging lens. However, in physics, the behavior of a lens is not just a property of the glass itself, but a result of the relative refractive index between the lens material and the surrounding medium. As noted in Science, Light – Reflection and Refraction, p.159, the speed of light changes as it moves between different media. It is this change in speed (refraction) at the interface that determines whether light rays bend toward or away from the principal axis.

The nature of a lens (converging or diverging) depends on whether the lens material is optically denser or rarer than the environment. If a lens is placed in a medium with a lower refractive index (like a glass lens in air), it behaves normally: a convex lens converges light and a concave lens diverges it Science, Light – Reflection and Refraction, p.151. However, if you submerge that same lens in a medium that is optically denser than the lens material itself, the direction of bending reverses. In such a case, a convex lens will actually cause light to diverge, effectively acting like a concave lens.

This principle is crucial for understanding how light behaves in complex environments like the human eye or underwater photography. If the refractive index of the medium equals the refractive index of the lens, the light does not bend at all; the lens effectively disappears and its focal length becomes infinite. This is why a glass rod can "disappear" when dipped into certain oils with the same refractive index.

Sources: Science, Light – Reflection and Refraction, p.151; Science, Light – Reflection and Refraction, p.159

7. Solving the Original PYQ (exam-level)