Relation between refractive index and speed of light

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Let us define refractive index first. When lightray of a particular color transfers from a transparent and homogeneous medium to another, the ratio of sine of incident angle and that of refractive angle is called the refractive index of the second medium w.r.t. the first. Refractive indices are of two types: absolute and relative.

When lightray passes from vacuum to another medium, absolute refractive index is considered. When lightray transfers between two transparent media other than vacuum, relative refractive index is considered. Such two media are glass and water. Absolute refractive index is always greater than 1, but relative refractive index can be greater or smaller than 1. Let us now tell about the relation between refractive index and speed of light. The relation is – inversely proportional. That means, the greater the refractive index of a medium is, the smaller is the speed of light in that. This relation is applicable both for relative and absolute refractive indices.

Suppose the absolute refractive index of a certain type of glass is 1.5, then it means that speed of light is 1.5 times greater in space/vacuum compared to that in glass. Again, relative refractive index of glass w.r.t. water is 1.128 – it means that speed of light is 1.128 times greater in water compared to that in glass. Generally speaking, if speed of light in vacuum is C and that in any other medium is Cm, then refractive index of that medium is, n = C/Cm.

Again, suppose the absolute refractive indices of two media a and b are na and nb respectively and speed of light in them are Ca and Cb respectively. Then na/nb = Cb/Ca.

It is wortfh to mention here that absolute refractive index of vacuum is 1 (unity). Another thing to note is that refractive index of a medium is associated with color of light. That’s because the same medium can have different refractive indices w.r.t. different colors of light.

In this regard, the order VIBGYOR need to be kept in mind. Whichever color is mentioned here earlier, absolute refractive index of a medium is greater for that. Just for example, if refractive index of a medium w.r.t. red light is 1.48, then that for violet light could be 1.52. Another point to note here is that during refraction, violet and it’s adjacent colors (like indigo and blue) will bend more compared to lights like orange and red.

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