SNELL’S LAW: Beyond the obvious 

Snell's Law Calculator

Snell’s Law is one of the first physics formulas students become acquainted with during their study of physics. Once optics makes its appearance, Snell’s law can perhaps be considered one of the most important formulas to be found in this area of study. While it is not a complicated idea to understand, the uses of this law extend well beyond a school textbook and are of profound benefit to the advancement of technology nowadays. If you are yet to study this topic, here is what you should know! 

Snell’s Law was named after a Dutch scientist of the 17th century called Willebrørd Snell (1580 – 1626). His work included mathematics, astronomy, and physics. While in mathematics he discovered a new way of calculating the value of π and was also involved in measuring the Earth by triangulation, it is his work on refraction that mostly lauded him with the recognition he has today. These laws however, were published posthumously, seventy years after his death, brought to light by the other Dutch physicist Christiaan Huygen. 

The question of refraction had occupied the minds of scientists throughout the centuries. It was ascertained, when an object was placed in water, it gave the illusion of appearing slanted, making it look distorted and at a different distance from the actual one. The conclusions put forward by the Greek astronomer Ptolemy to mathematically define this phenomena were further developed by Snell. The observations started when Snellius noticed that a ray of light bent when it entered a block of glass. The angle it made when entering the surface (incident angle) influenced the angle by which light would bend. 

  So what does the law actually mean? Snell’s law states that “the ratio of the angle of incidence and the angle to the angle of refraction of a wave traveling across a boundary is known as the refractive index”. Snell’s law is basically also known as the law of refraction, providing us with a method to predict the amount by which an angle will bend, while also presenting us with an important property of any one specific medium, the refractive index, categorized as n, which determines the aforementioned physical observation of the bending of light. The refractive index is constant for a given medium. The angles of incidence and refraction are related to each other by the ratio of their sines. Rearranging the formula yields a better view of this ratio existing between the indexes of refraction and the respective angles, which are directly proportional to each other. If the wave travels from a medium of a higher refractive index to one of a lower refractive index, the wavelength of the light will decrease and this will trigger the speed to decrease, while it will be witnessed that the ray of light will bend towards the normal. 

n1sin1 = n2sin2

n = n1n2= sin2sin1 

Several other phenomena and concepts arise from the basics of Snell’s Law. A well-known one, currently employed in a myriad of technological and scientific apparatuses is Total Internal Reflection (TIR). In some cases, the angle of refraction might be equal to 90º degrees (the maximum possible angle of refraction), if this happens then the corresponding angle of incidence is termed the critical angle. If the angle of incidence exceeds the critical angle value, there will be no refraction but, on the other hand, the light will be reflected and will not escape the incident medium. This is denominated as Total Internal Reflection. The other requirement for this phenomenon to occur implies to travel from a denser to a less dense medium. Optical fibers work through the principle of TIR. These are used in communication systems and micro-surgeries, allowing to transmit light without losing energy or the system’s signal. 

If one ever explores the world of medical physics, optics is one of the most important components that have made much of the equipment used in hospitals and laboratories feasible. One such instrument is the one employed in an endoscopy, which is a non-surgical procedure that is used to examine a patient’s digestive tracts. The endoscope consists of optical fibers, and with what was explained before, uses the concept of total internal reflection to allow light through curved paths, without any outside refraction. The doctor is then able to view pictures of the digestive tract on a color TV monitor. Endoscopes are considered to be one of the most significant medical instruments. 

You can now appreciate the important Snell’s law and the concept of refraction. Not only in explaining various phenomena in both large and small scale situations but also in the use it has been put to. Whether it is for optical instruments or for new technology, Snell’s law is something that is continually present in the study and practical use of physics.

Writer: Maria Esther Vilar Alvarez

Editor: Omar Alturki/ Yara Bawazir


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  3. Davidson, Michael W. “Willebrord Snell.” Molecular Expressions: Science, Optics and You – Timeline – Willebrord Snell, Florida State University,
  4. Fellers, Thomas J., and Michael W. Davidson. “Introduction to the Refraction of Light.” Refraction of Light – Introduction , Olympus LS,
  5. “Physics Tutorial: Total Internal Reflection.” The Physics Classroom,