The **Snell ‘s law** in a **formula** used to determine the **relationship** that exists between the path taken by a beam of light crossing the **boundary** or the surface of **separation** between two contact substances and the refractive index of each of they. This law was discovered in 1621 by the Dutch astronomer and mathematician **Willebrord Snell** . Snell’s account of the law was not published until Christiaan Huygens mentioned it in her treatise on light.

## What is Snell’s Law?

Snell’s law is a **formula** that is used to calculate the **angle** of **refraction** that light has when it passes through the separation **surface** that exists between two different media.

- What is Snell’s law?
- History
- Snell’s law statement
- Formula
- Refraction
- Snell’s law applications
- Optical fiber
- Examples

## What is Snell’s law?

Before explaining what Snell’s law consists of, it is important to also know the definition of **refraction** of light. This term refers to the change of **direction** that a **wave** can experience when it passes from one material medium to another. This change can only be caused if the wave is **obliquely** incident on the area of separation of the two media and if they have different refractive indices.

Then, Snell’s law consists of a **formula** that is used particularly to achieve the calculation of the **angle** of **refraction** of light when it passes the separation surface that exists between two media that have a different refractive index. The law then explains that the product of the **index** of refraction times the sine of the angle of incidence is **constant** for any **ray** of light incident on the surface of two media.

## History

**Willebrord Snell ****van Royen** was a **Dutch-** born astronomer and mathematician who was born in 1580 in Leiden and died in 1626. He began to study law but his main interest was mathematics . He also showed great interest in the study of physics and astronomy and in 1615 created a method to measure the **radius** of the earth.

In the year **1621 he** promulgated the **law of refraction** which was a simple formula to calculate the angle of refraction of light when it passes through a surface that separates two media with different refractive index.

It was apparently first mentioned by **Ibn Sahl** in the 10th century. In 1601 the term was taken into consideration again by **Thomas Harriot** , but he did not publish it. The law was also described by **René Descartes** . Many scientists had analyzed that light rays changed direction when they came into contact with a denser surface, but Snell discovered the exact law in **1621** .

## Snell’s law statement

The statement of Snell’s law tells us that the **product** of the index of **refraction times** the **sine** of the **angle of incidence** is constant for any ray of light striking the **separating** surface of two media. Although this law was created with the objective of being able to explain the phenomena of refraction of light, it can also be applied to all types of waves that are crossing a separation surface between two media in which the speed of propagation of the wave varies.

## Formula

The formula used to apply Snell’s law is the following:

**n1. sin i = n2. sin t,** where:

- i—>
**incident angle**(it is the angle that the incident ray makes with the normal N). - t—>
**transmitted angle**(it is the angle that the transmitted ray makes with the normal N). - n1–> indicates the
**refractive index of**the first medium. - n2–> shows the refractive index of the second medium.

From the above equation it follows that when **n2 <n1** there is an angle of incidence, called the limit angle, from which refraction does not occur -> **Total reflection** .

**i_L–> limit angle: i_L = arc sin (n2 / n1);**

## Refraction

Refraction, in the field of **physics** , refers to the **change** that occurs in the **direction** of a **wave** that passes from one medium to another caused by its change in speed. Light is refracted each time it travels at an angle towards a substance with a different refractive index, which is what we know as **optical density** . This change in direction is caused by a change in **speed** .

## Snell’s law applications

Refraction allows us to have lenses, magnifying glasses, prisms, and rainbows. Even our eyes depend on this curvature of light. Without refraction, we would not be able to focus light on our retina.

## Optical fiber

Fiber optics is a **transmission** medium that is used mainly in **data networks** . It consists of a very thin **wire** of **plastic** or **glass** material through which **pulses** of light or data are sent to be transmitted. The beam of light travels through the fiber through an angle of reflection that passes above the angle that is the limit of total reflection. This light source that is used can be a **laser** or also an **LED light** .

Otic fibers are widely used in **telecommunications** as they have the advantage of being able to carry information over long distances at fairly fast speeds.

## Examples

Some examples of Snell’s law are:

- When we observe a
**mirage**, they are caused by extreme cases of refraction of light, and it is known by the name of total reflection. - When we observe the mountains or trees
**reflected**in the waters of rivers or lakes. - In
**optical fibers**.