Conceptual Index of Refraction Question.

[fallen186]

We have the index of refraction formula of $$n = \frac{c}{v}$$ which essential states how much of a factor light travels faster in a vacuum than in this medium. Why don't they just have it as $$n=\frac{v}{c}$$ so it states fractionally how much slower light travels in the medium than the speed of light.

Its like saying light in a vacuum is going 1.5 times faster than it would if it was in glass compared to "light going through glass is 2/3 slower than going in a vacuum".

I feel like it would be simpiler to just to say 2/3, and less confusing.

 

[Redbelly98]

I agree with you.

However, Snell's Law for the refraction of light predates the first reasonable measurement of the speed of light. The index of refraction was initially used to explain light refraction at an interface, and the speed of light was not a consideration in its definition.

 

[kerimek]

Thank you for your question. The index of refraction formula, n = c/v, is a fundamental equation in optics that relates the speed of light in a vacuum (c) to its speed in a medium (v). This formula is based on the observation that light travels slower in a medium due to interactions with the atoms and molecules in the material. The index of refraction, n, is a unitless quantity that represents the ratio of the speed of light in a vacuum to its speed in the medium.

While it may seem simpler to express the index of refraction as a fraction, such as v/c, this would not accurately represent the relationship between the two speeds. The index of refraction is not simply a measure of how much slower light travels in a medium, but rather a measure of the degree to which the speed of light is affected by the medium. This is why the formula is written as n = c/v, to emphasize the ratio between the two speeds rather than a fractional difference.

Furthermore, the index of refraction is a fundamental property of a material and is not affected by the specific wavelength or color of light. Expressing it as a fraction would not accurately reflect this property. In summary, while it may seem simpler to express the index of refraction as a fraction, the current formula n = c/v accurately represents the relationship between the speed of light in a vacuum and in a medium.