angle of refraction
The angle between the perpendicular and a ray refracted at a surface
angle of refraction: the bend measured from the normal
When light crosses from one transparent medium into another, its path bends. The angle of refraction is the angle between the refracted ray and the normal, which is an imaginary line perpendicular to the surface at the point of incidence. This angle tells you how far the light has bent after entering the new medium.
The relationship between the angle of incidence and angle of refraction is governed by Snell's law: n1 sin(θ1) = n2 sin(θ2), where n represents the refractive index of each medium and θ represents the respective angles from the normal. Light bends toward the normal when entering a denser medium (higher refractive index) and away from the normal when entering a less dense medium. Air has a refractive index of approximately 1.0; glass ranges from 1.5 to 1.9 depending on composition; water is about 1.33.
Practical measurement and use
In optical design, the angle of refraction determines where light rays converge or diverge after passing through lenses, prisms, and windows. A lens's focal length and magnification depend directly on how much refraction occurs at its curved surfaces. In precision manufacturing, refractometers measure the refractive index of liquids by observing the critical angle where refraction changes behavior abruptly. Fiber optic systems rely on controlling refraction angles to keep light bouncing down glass cores thinner than human hair.
One common problem is chromatic aberration, where different wavelengths refract at slightly different angles because refractive index varies with color. This causes colored fringes at edges in lenses and must be corrected by combining different types of glass. Similarly, total internal reflection occurs when light traveling from a denser to less dense medium hits the surface at an angle steeper than the critical angle; refraction stops entirely and light bounces back.
The term comes from the Latin refringere, meaning to break, because refraction appears to break or bend the path of light. Historically, the law of refraction was discovered empirically by Willebrord Snell in the 1620s, though it had been approximated much earlier. Today it is fundamental to every optical device: cameras, microscopes, telescopes, and industrial vision systems all depend on controlling the angle of refraction to focus or redirect light precisely.