Snell's Law
When light crosses the boundary between two media, it bends. The relationship between the angle of incidence and the angle of refraction is governed by Snell's law — a simple equation that explains everything from how a straw looks bent in water to why diamonds sparkle.
n1 sin θ1 = n2 sin θ2
Snell's law
Snell's law (also called the Snell-Descartes law) describes how a light ray changes direction when crossing the interface between two media with different refractive indices. The law states: n₁ sin θ₁ = n₂ sin θ₂, where n₁ and n₂ are the refractive indices and θ₁, θ₂ are the angles measured from the normal (perpendicular) to the surface.
Total internal reflection
When light travels from a denser medium (higher n) to a less dense one (lower n), there exists a critical angle beyond which no refracted ray exists. At this angle, sin θ₂ would need to exceed 1, which is impossible. All the light is instead reflected back into the denser medium. This phenomenon, called total internal reflection (TIR), is what makes fiber optics work and causes the shimmering surface you see when looking up from underwater.
Reflection
At any interface, some light is always reflected. The reflected ray obeys the law of reflection: the angle of reflection equals the angle of incidence, both measured from the normal. The proportion of reflected versus refracted light is given by the Fresnel equations, which depend on the polarization of the light. In this simulation, we show the reflected ray with reduced intensity (dashed line) to keep the focus on refraction.
Historical note
Though named after Dutch astronomer Willebrord Snellius (1580–1626), the law was first accurately described by the Persian scientist Ibn Sahl in 984 CE, over 600 years earlier, in his treatise On Burning Mirrors and Lenses.