Law of Refraction or Snell’s Law- Formula, Rules, and Discovery

Have you ever seen a bent pencil in a glass of water? Have you ever wondered why that is? It is because of the refraction (law of refraction). The speed of light is different from medium to medium. When light travel’s through a vacuum (space) it is faster than in the earth’s atmosphere, and even more, its speed is less in the glass of water than in the atmosphere.

How The Law of Refraction Works

The Law of refraction is used to determine the direction of light rays. When light enters from a vacuum to glass it slightly bends, and this bending of light from varying objects and mediums is called refraction.


n1 sin θ1 = n2 sin θ 2
n1 = incident index
n2 = refracted index
θ1 = incident angle
θ2 = refracted angle

Discovery of Law of Refraction

In 1621 Willebrørd Snell discovered the law of refraction. The law of refraction is also known as Snell’s law. However, if we go all the way back in 1021 a mathematician and astronomer by the name of Alhazen (in Arabic Hasan Ibn al-Haytham, full name Abū ʿAlī al-Ḥasan ibn al-Ḥasan ibn al-Haytham أبو علي، الحسن بن الحسن بن الهيثم; c. 965 – c. 1040) published his book “Book of Optics” ((Arabic: كتاب المناظر, “Kitāb al-Manāẓir”) and he mentioned the bending of light in water and other similar issues and their reasons.

In 984 a Persian mathematician and physicist Ibn Sahl (full name Abū Saʿd al-ʿAlāʾ ibn Sahl أبو سعد العلاء ابن سهل; c. 940–1000) accurately described the refraction in the manuscript “On Burning Mirrors and Lenses”. We do have evidence of his own written manuscript below.

Ibn Sahl manuscript - GMISR
Ibn Sahl’s manuscript showing the calculations of snell’s law in 984

In 1602 an English astronomer and mathematician, Thomas Harriot rediscovered Snell’s law, but he did not publish it.


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