# What is the relation between wavelength and refractive index?

By BYJU'S Exam Prep

Updated on: September 25th, 2023

The relation between wavelength and refractive index is stated to be inversely proportional to the wavelength. The wavelength is a characteristic of waves that determines the separation between similar places between two subsequent waves. Wavelength is denoted by λ (lambda). It has the following mathematical representation:

v = λf (equation 1)

Here,

• The speed of light is v.
• The frequency of light is f.

### Relation between Wavelength and Refractive Index

• The refractive index describes how much a light beam bends when moving between two different media.
• Indicating the refractive index is n.

It has the following mathematical representation:

n = c/v (equation 2)

The speed of light in a vacuum, c, is used here.

The speed of light in a medium is given by v.

Equation 1 can be used for equation 2 to determine the relationship between wavelength and refractive index.

n = c/ λf

• The rate at which the refractive index changes in a material with respect to distance is known as the refractive index gradient. The slope of the refractive index profile at any given location is referred to as distance.
• The reciprocal of a unit of distance is used to express the refractive index gradient.
• An example of a refractive index gradient is the rate at which the refractive index changes with distance at any certain place.

As a result, it is claimed that the wavelength and the refractive index are inversely related.

Summary:

## What is the relation between wavelength and refractive index?

The refractive index is said to be inversely proportionate to the wavelength in terms of their relationship. The gradient of the refractive index is a vector point function.

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