# Refractive index

The refractive index is a dimensionless quantity that measures the ratio between the speeds of light in different media.

**Refractive index**

**is**the ratio of the

**speeds**of light between two media through which it travels. The

**absolute**

**refractive**

**index**

**,**in turn, is calculated with reference to the

**vacuum**, the medium through which light propagates with the greatest possible speed. Therefore, we can say that this index measures how many times the speed of light is greater in a vacuum than in other media, while the

**relative**

**refractive**

**index**

**is**defined as the ratio between the speeds of light between

**any two media**.

The refractive index is a scalar , **dimensionless** quantity whose **modulus** is always greater than or equal to **1** . For example, the speed of light in a vacuum is 1.33 times greater than that of light traveling in a medium whose refractive index is 1.33. Furthermore, there is no knowledge of any medium in which light travels faster than in a vacuum.

Furthermore, the refractive index depends directly on the frequency of light incident on the medium. Generally, the **higher the frequency of light** , **the higher the refractive index** of light for that specific frequency. It is for this reason that light is **dispersed** and begins to display the colors of the visible spectrum, for example, when propagating through a prism.

**How to calculate the refractive index?**

The refractive index can be calculated by the following formula, please note:

**Subtitle:**

**n** — refractive index

**c** — speed of light in vacuum

**v** — speed of light in the medium

In the equation just presented, **c** is the speed of light in vacuum, whose magnitude is approximately 299,792,458 m/s (3.0 x ^{10 8} m/s), about three hundred million meters per second. The variable **v** is the speed of light in the other media in which it propagates, such as in air, water or glass. We say that a medium that has a higher refractive index than the refractive index of other media is more **refractive.**

**Examples**

Check out some solved examples that show us how it is possible to make calculations related to the refractive index:

**1)** Let’s calculate the refractive index of light that propagates inside a diamond. To do so, consider that, inside the diamond, light propagates with a speed of 1.25 x ^{10 8} m/s, see how:

The result indicates that, in a vacuum, light travels 2.4 times faster than inside a diamond.

**2)** A certain transparent and homogeneous medium has an absolute refractive index of 1.2. Determine the speed at which light travels through it.

**Data** : c = 3.0.10 ^{8} m/s

**Refractive index table**

Check out a table that presents the refractive indices of some known materials:

Material |
Refractive index |

Air | 1.0003 |

Water | 1.33 |

Ice | 1.31 |

Alcohol | 1.36 |

Oil | 1.46 |

crown glass |
1.52 |

Diamond | 2.42 |

Ruby | 1.71 |

**Absolute and relative refractive index**

**We call the absolute** refractive index the ratio between the speeds of light in a vacuum and in a given medium. **The relative** refractive index , in turn, is defined as the ratio between the speed of light that propagates between two media, provided that one of them is not a vacuum.

We can calculate the relative refractive index using the following equation:

In this equation, the medium, whose index of refraction is given by n _{1} , is the medium from which the light comes, while the medium of refractive index n _{2} is the medium towards which the light is directed.

**Exercises solved**

**1)** In a certain transparent material, light propagates with a speed equal to 0.8c, being c the speed of light in vacuum. Determine the refractive index of this material.

**Resolution:**

To solve this exercise, we will use the refractive index formula:

**2)** In a certain material, light travels at 75% of the speed of light. Determine the refractive index of this material.

**Resolution:**

To solve the exercise, we need to consider that 75% of the speed of light can be written as 0.75c, where c represents the speed of light in vacuum. Next, we will use the refractive index formula:

**3)** Light propagates between two media of different refractive indices. On its way, light emerges from a medium whose index of refraction is 1.5 towards a medium whose index of refraction is 1.25. Determine the relative refractive index for these two media.

**Resolution:**

Using the refractive indices informed in the statement, we will calculate the relative refractive index according to the following calculation:

The result obtained — 1.2 — indicates that the speed of light is 20% greater in medium 2 than in medium 1.