Considering different media, in which of the following does light travel with the greatest speed?

Introduction / Context:

The speed of light is a fundamental constant in physics, but its value depends on the medium through which it travels. In competitive exams, questions often ask where light travels fastest or slowest among different media such as vacuum, air, water and solids. This question tests whether you know that the maximum speed of light is achieved in vacuum and that light slows down when it passes through material media.

Given Data / Assumptions:

• c denotes the speed of light in vacuum, approximately 3 × 10^8 m s^-1.
• In a medium with refractive index n, the speed of light v is given by v = c / n.
• The refractive index of vacuum is exactly 1.
• The refractive indices of air, water and solids like steel are greater than 1.

Concept / Approach:

The refractive index n of a medium is defined as n = c / v, where c is the speed of light in vacuum and v is the speed of light in that medium. Rearranging gives v = c / n. Since n is always greater than or equal to 1, the speed of light is maximum when n is minimum. The smallest possible refractive index is 1, which occurs in vacuum. In air, n is slightly greater than 1, so light is slightly slower than in vacuum. In water and solids like glass or steel, n is significantly larger than 1, so light slows down even more. Therefore, the medium in which light travels fastest is vacuum.

Step-by-Step Solution:

Verification / Alternative check:

Standard data tables show that the speed of light in air is about 3.0 × 10^8 m s^-1 multiplied by a small factor less than 1, such as 0.9997, while in water it is around 2.25 × 10^8 m s^-1, and in glass even lower. Metals like steel are opaque for visible light, but where propagation is considered, effective speeds are much lower than in transparent media. All of this confirms the general rule that light travels fastest in vacuum and slows down in any material medium.

Why Other Options Are Wrong:

Option A (nitrogen gas): Nitrogen gas is very similar to air in refractive index and still has n slightly greater than 1, so light is slower than in vacuum.

Option B (air at sea level): Light speed in air is slightly less than in vacuum due to n being slightly above 1.

Option C (steel): Visible light does not propagate freely through steel; metals strongly interact with light, and any effective propagation speed is much lower than in vacuum.

Option E (water): Water has n about 1.33, so light speed in water is about c / 1.33, clearly less than c.

Common Pitfalls:

Because the difference in speed between vacuum and air is small, some students mistakenly think they are exactly the same. While for many practical purposes light speed in air can be approximated by c, conceptually and in exam questions the maximum speed is in vacuum. Remember the simple rule: as refractive index increases, speed of light decreases. Vacuum, with the smallest possible refractive index of 1, gives the highest speed.

Final Answer:

Light travels fastest in vacuum.