What does the index of refraction measure?

The index of refraction is a critical parameter in optics that quantifies how much the speed of light is reduced when it travels through a given medium compared to its speed in a vacuum. Specifically, it is defined as the ratio of the speed of light in a vacuum to the speed of light in the medium. This is why the option regarding the speed of light in an optical medium is the correct choice.

A higher index of refraction indicates that light travels slower in that medium, which affects various optical properties such as the bending of light (refraction) when it enters or exits the medium. Understanding the index of refraction is fundamental in fields like fiber optics, where it impacts the design and performance of optical systems. For instance, it determines how light propagates through optical fibers, influencing loss, bandwidth, and overall efficiency.

The other options, while related to optical fibers, do not define the index of refraction. The diameter of the optical fiber core deals with the physical dimensions of the fiber, the length of the optical fiber pertains to the distance the light travels, and the number of modes supported by the fiber relates to its ability to carry multiple light paths, which is influenced by its refractive index but does not directly define it.