Snell’s Law


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.


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.


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, 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.


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 .

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