Question:
Define refractive index of a medium in terms of speed of light.
Define refractive index of a medium in terms of speed of light.
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Refractive index is a pure number with no units. If a medium has a higher refractive index, it is optically denser, meaning light travels slower inside it ($v = c/\mu$).
Updated On: Jul 2, 2026
- It is the ratio of the speed of light in a vacuum to the speed of light in the medium.
- It is the ratio of the speed of light in the medium to the speed of light in a vacuum.
- It is the product of the speed of light in a vacuum and the speed of light in the medium.
- It is the reciprocal of the speed of light in a vacuum.
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The Correct Option is A
Solution and Explanation
Concept:
The absolute refractive index ($n$ or $\mu$) of an optical medium is a dimensionless fundamental property that quantifies how much the speed of light is reduced inside that medium relative to a vacuum. It acts as a measure of the optical density of the medium.
When an electromagnetic wave passes from an empty space (vacuum) into a material medium, its interactions with the electronic structure of the atoms or molecules cause a net reduction in its phase velocity. The relation is expressed mathematically as:
$$\mu = \frac{c}{v}$$
Where:
• $c$ represents the speed of light in a vacuum (approximately $3 \times 10^8 \text{ m/s}$).
• $v$ represents the speed of light in the specific material medium. Since $c$ is always greater than or equal to $v$ in any physical material medium, the absolute refractive index $\mu$ is always greater than or equal to $1$ ($\mu \ge 1$). Being a ratio of two identical physical quantities (speeds), it has no units or dimensions.
Step 1: Formal Definition Expression.
By structural definition, the absolute refractive index ($\mu$) of a given medium is defined as the ratio of the velocity of light in a vacuum (or air as a close approximation) to the velocity of light in that particular medium. $$\mu = \frac{\text{Speed of light in vacuum }(c)}{\text{Speed of light in medium }(v)}$$ Since this perfectly matches statement (A), the conceptual definition is established directly.
• $c$ represents the speed of light in a vacuum (approximately $3 \times 10^8 \text{ m/s}$).
• $v$ represents the speed of light in the specific material medium. Since $c$ is always greater than or equal to $v$ in any physical material medium, the absolute refractive index $\mu$ is always greater than or equal to $1$ ($\mu \ge 1$). Being a ratio of two identical physical quantities (speeds), it has no units or dimensions.
Step 1: Formal Definition Expression.
By structural definition, the absolute refractive index ($\mu$) of a given medium is defined as the ratio of the velocity of light in a vacuum (or air as a close approximation) to the velocity of light in that particular medium. $$\mu = \frac{\text{Speed of light in vacuum }(c)}{\text{Speed of light in medium }(v)}$$ Since this perfectly matches statement (A), the conceptual definition is established directly.
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