Snell's law
the law that, for a ray incident on the interface of two media, the sine of the angle of incidence times the index of the refraction of the first medium is equal to the sine of the angle of refraction times the index of refraction of the second medium
Snell's law: why light bends at material boundaries
When light crosses the boundary between two materials with different optical densities, its path bends. Snell's law quantifies this bending mathematically: n₁ sin(θ₁) = n₂ sin(θ₂), where n is the refractive index of each medium and θ is the angle the ray makes with the normal (perpendicular) to the interface. This relationship holds at every interface where light changes media, from air into glass, water, or any transparent material.
The refractive index is a material property that measures how much it slows light compared to vacuum. Vacuum has n = 1.0; air approximates this at 1.0003; water is 1.33; common optical glass ranges from 1.5 to 1.9. When light moves from a slower medium to a faster one (lower to higher n), it bends away from the normal. Moving from faster to slower, it bends toward the normal. The greater the difference in refractive indices across an interface, the more dramatic the bending.
Critical angle and total internal reflection
At sufficiently shallow incident angles, light traveling from a denser medium toward a less dense one will not exit at all. Instead, it reflects entirely back into the first medium. This occurs beyond the critical angle, defined by sin(θc) = n₂/n₁. For light traveling from glass (n = 1.5) to air (n = 1.0), this critical angle is about 42 degrees. This principle is essential in fiber optics, prisms, and optical guides, where total internal reflection confines light within a dense material and prevents unwanted escape.
Optical designers use Snell's law to calculate the path of light through lens systems, determine focal lengths, and correct for chromatic aberration, which arises because refractive index itself varies slightly with wavelength. Precision measurements of refractive index rely on observing refraction angles and applying the law in reverse. Quality control of optical materials often includes refractometry, a direct application of this principle.
The law is named for Willebrord Snellius, a 17th century Dutch mathematician, though the principle was known earlier to Islamic and European scholars. In modern optics it is sometimes called the law of refraction, and it forms the foundation of geometrical optics, which treats light as rays obeying simple mechanical rules. It breaks down only at extremely high intensities (nonlinear optics) or when dealing with very short wavelengths approaching atomic scales.