In optics, the refractive index of a substance is described by the formula n = c/v, where c is:

the speed of light in vacuum

The correct answer is option 4. the speed of light in vacuum.

In optics, the refractive index (\(n\)) of a substance describes how much light is slowed down when passing through that substance compared to its speed in a vacuum. The refractive index is calculated using the formula:

\[n = \frac{c}{v}\]

Where:

\(n\) is the refractive index of the substance.

\(c\) is the speed of light in vacuum.

\(v\) is the speed of light in the medium.

Now, let's explain each component of the formula:

1. Speed of Light in Vacuum (\(c\)):

\(c\) represents the speed of light in vacuum, which is approximately 299,792,458 meters per second (m/s).

Light travels at its maximum speed in a vacuum because there are no particles or medium to interact with.

2. Speed of Light in the Medium (\(v\)):

\(v\) represents the speed of light in the substance or medium.

The speed of light in a medium is typically less than the speed of light in vacuum because light interacts with the particles of the medium, which slows it down.

The refractive index indicates how much slower light travels in the medium compared to its speed in vacuum. A higher refractive index implies greater slowing down of light in the medium.

3. Relationship between Refractive Index and Speed of Light:

The refractive index (\(n\)) is defined as the ratio of the speed of light in vacuum (\(c\)) to the speed of light in the medium (\(v\)).

When the refractive index is greater than 1, it indicates that light travels more slowly in the medium compared to vacuum.

Different substances have different refractive indices, and this property is fundamental in understanding various optical phenomena such as refraction, reflection, and dispersion.

In summary, the refractive index (\(n\)) of a substance in optics is described by the formula \(n = \frac{c}{v}\), where \(c\) represents the speed of light in vacuum. This formula quantifies how much light is slowed down when passing through a substance compared to its speed in vacuum, and the refractive index is a key parameter in understanding optical behavior in different materials.