Snell's Law

Introduction

Snell's law, also known as the law of refraction, is a fundamental principle in the field of optics that describes how light or any other wave behaves when it transitions from one medium to another. The law is named after the Dutch astronomer Willebrord Snellius, who formulated it in 1621.

Historical Background

The concept of refraction has been understood since ancient times, with early descriptions appearing in the works of Greek philosophers such as Euclid and Ptolemy. However, the mathematical formulation of the law was not established until the 17th century by Snellius.

Mathematical Formulation

The mathematical representation of Snell's law is given by the equation n1*sin(θ1) = n2*sin(θ2), where n1 and n2 are the indices of refraction for the two media, and θ1 and θ2 are the angles of incidence and refraction, respectively, measured from the normal to the interface between the two media.

Derivation from Fermat's Principle

Snell's law can be derived from Fermat's Principle of Least Time, which states that light travels along the path that takes the least time. This principle is a fundamental concept in the field of optical physics.

Applications

Snell's law has wide-ranging applications in various fields such as optics, geology, and astronomy. It is fundamental to the operation of optical devices such as lenses and prisms, and is used in the analysis of seismic waves in geology.

Limitations and Extensions

While Snell's law accurately describes the behavior of light in most situations, there are circumstances where it fails, such as in the case of total internal reflection and when dealing with anisotropic materials. Extensions to Snell's law have been developed to handle these situations.