The speed of light in a certain medium is V while its speed in a vacuum is C. The absolute refractive index of the medium is

Analyze the question: You are asked for the absolute refractive index of a medium, given the speed of light in that medium (V) and in a vacuum (C).

Concept: The absolute refractive index (n) of a medium is the ratio of the speed of light in a vacuum to the speed of light in that medium:

This is the same as the ratio sin i / sin r when light passes from a vacuum (or air) into the medium.

Solution:

• Speed in vacuum = C
• Speed in the medium = V

Check the options:

• A (C + V) and D (C − V): refractive index is a ratio, so adding or subtracting speeds is wrong.
• C (V/C): this is the inverse. It would be less than 1, but the refractive index of any material medium is always greater than 1, because light travels more slowly in a medium than in a vacuum (V < C).
• B (C/V): correct, and it gives a value greater than 1.

Tip: Remember "vacuum over medium", with the fastest speed on top. This is why the refractive index is never less than 1. For example, glass has n = 1.5, which means light travels 1.5 times slower in glass than in a vacuum. Also note that refractive index has no unit, since it is a ratio of two speeds.