In optics, the refractive index of a transparent medium is defined in terms of the speed of light. Which of the following correctly gives this definition?

Introduction / Context:
This question tests your knowledge of the basic definition of refractive index in geometrical optics. The refractive index describes how much the speed of light is reduced in a medium compared to vacuum and determines how much light bends when entering or leaving that medium. Many formulas in optics, including Snell law, use refractive index as a key parameter, so it is important to know its correct definition in terms of speeds.

Given Data / Assumptions:

• We consider a transparent medium such as glass, water or air.
• c denotes the speed of light in vacuum, and v denotes the speed of light in the medium.
• The refractive index is represented by n.
• We are asked to choose the correct expression relating n, c and v.

Concept / Approach:
The absolute refractive index n of a medium is defined as the ratio of the speed of light in vacuum to the speed of light in that medium: n = c / v. Since light travels fastest in vacuum, c is the maximum speed. In any material medium, v is less than c, so n is greater than or equal to 1. This definition reflects how much the medium slows down light. Expressions involving the ratio reversed (v / c) or the product c * v are incorrect. Therefore, refractive index is correctly defined as c divided by v, or in words, the ratio of speed of light in vacuum to the speed of light in the medium.

Step-by-Step Solution:
Step 1: Let c be the speed of light in vacuum, which is approximately 3 * 10^8 m/s. Step 2: Let v be the speed of light in the given medium, for example, in glass or water. Step 3: The absolute refractive index n of the medium is defined as n = c / v. Step 4: Because v is always less than or equal to c, n is always greater than or equal to 1, which matches physical expectations. Step 5: Compare this with the options; the one that states the ratio of speed of light in vacuum to the speed of light in the medium is correct. Step 6: Reject options mentioning the inverse ratio or product, as they do not match the standard definition.

Verification / Alternative check:
Consider light in water, where the refractive index is approximately n ≈ 1.33. This means that light travels about 1.33 times faster in vacuum than in water, so v = c / 1.33. If we were to define n as v / c, then n would be less than 1, which contradicts the standard values listed in optical tables. Similarly, defining n as a product has no physical meaning in this context. The fact that known refractive indices for common materials are greater than 1 confirms that n must be defined as c / v, not its inverse.

Why Other Options Are Wrong:
Defining refractive index as the ratio of speed of light in the medium to the speed of light in vacuum (v / c) would produce values less than 1 for typical media, in conflict with standard refractive index data. Defining it as the product of speeds (c * v) has no conventional meaning in optics and is dimensionally inconsistent with a dimensionless refractive index. None of above is incorrect because the option defining refractive index as the ratio c / v is correct and widely accepted.

Common Pitfalls:
Students sometimes invert the ratio mistakenly and think n = v / c, often due to misremembering the definition. A useful way to avoid this is to recall that refractive index is greater than or equal to 1 for any medium, with n = 1 in vacuum. This can only be true if n = c / v, since v cannot exceed c. Focusing on this inequality helps you remember the correct ratio even if you forget the exact wording.

Final Answer:
The refractive index of a transparent medium is defined as the ratio of the speed of light in vacuum to the speed of light in the medium, that is n = c / v.