{"id":408,"date":"2026-07-03T02:50:19","date_gmt":"2026-07-03T02:50:19","guid":{"rendered":"https:\/\/physicsfundamentalsinfo.com\/blog\/?p=408"},"modified":"2026-07-13T23:30:05","modified_gmt":"2026-07-13T23:30:05","slug":"snells-law-explained","status":"publish","type":"post","link":"https:\/\/physicsfundamentalsinfo.com\/blog\/mechanics\/snells-law-explained\/","title":{"rendered":"Snell’s Law Explained"},"content":{"rendered":"\n
Definition<\/div>

\n\nSnell’s law states that when light passes from one transparent medium into another, n1<\/sub> sin \u03b81<\/sub> = n2<\/sub> sin \u03b82<\/sub>: the refractive index of each medium multiplied by the sine of its ray’s angle from the normal is equal on both sides of the boundary. It predicts exactly how much a light ray bends when it crosses between materials.\n\n<\/p><\/div>\n\n

Push a straw into a glass of water and it appears to snap sideways at the surface. Kneel at the edge of a swimming pool and the bottom looks temptingly close \u2014 then you jump in and discover it is a good third deeper than it looked.<\/p>\n\n

Neither the straw nor the pool is broken. Light simply changes direction the instant it crosses between water and air, and Snell’s law is the rule that says exactly how far it swings. By the end of this guide you will be able to calculate that swing in seconds \u2014 and spot the traps that catch most students.<\/p>\n\n

What Is Snell’s Law?<\/h2>\n\n

Strip away the Greek letters and Snell’s law says something surprisingly tidy: every transparent material gets a number, and that number decides how sharply light bends on the way in or out. The number is the refractive index<\/strong>, n \u2014 a measure of how much a material slows light down.<\/p>\n\n

Formally, Snell’s law (also called the law of refraction<\/strong>) states that for a ray crossing the boundary between two media, the product of refractive index and the sine of the ray’s angle \u2014 always measured from the normal<\/em>, the line perpendicular to the surface \u2014 is the same on both sides. One boundary, one equation, one unknown: that is why examiners love it.<\/p>\n\n

The direction of the bend follows a simple pattern. Entering a slower, optically denser medium (air into water, say), the ray bends toward<\/strong> the normal; heading back out into a faster medium, it bends away<\/strong> from it.<\/p>\n\n

Who Discovered Snell’s Law?<\/h3>\n\n

The name is an accident of history. The law was first accurately described in 984 CE by Ibn Sahl, a mathematician working in Baghdad, who used it in his treatise on burning mirrors and lenses to design lens shapes that focus light without geometric aberration.<\/p>\n\n

It was then rediscovered independently several times: by Thomas Harriot in 1602 (unpublished), by the Dutch astronomer Willebrord Snellius in 1621 (also unpublished in his lifetime), and by Ren\u00e9 Descartes, who finally published it in 1637 \u2014 which is why in France it is known as the Snell\u2013Descartes law<\/a>.<\/p>\n\n

The Snell’s Law Formula<\/h2>\n\n

Here is the equation in its standard form:<\/p>\n\n

n1<\/sub> sin \u03b81<\/sub> = n2<\/sub> sin \u03b82<\/sub><\/div>\n\n