Apply Snell's Law to calculate refraction angles, critical angles, and total internal reflection. Includes a live ray diagram and step-by-step solution.
The critical angle exists when light travels from a denser medium to a less dense one (nβ > nβ). Beyond this angle, total internal reflection occurs.
Find the unknown refractive index given the other index and both angles.
Calculate the speed of light in a medium from its refractive index. Speed = c Γ· n.
| Material | n |
|---|---|
| Vacuum | 1.0000 |
| Air (20Β°C) | 1.0003 |
| Water | 1.333 |
| Ethanol | 1.362 |
| Crown glass | 1.52 |
| Flint glass | 1.62 |
| Diamond | 2.417 |
Refraction is the bending of light (or any wave) as it passes from one medium to another with a different refractive index. When light moves from air into water, it slows down and bends toward the normal (the perpendicular to the surface). When it moves from water to air, it speeds up and bends away from the normal. This is why a straw in a glass of water appears bent.
Snell's Law describes the relationship between angles of incidence and refraction: nβ sin ΞΈβ = nβ sin ΞΈβ. Here nβ and nβ are the refractive indices of the two media, and ΞΈβ and ΞΈβ are the angles measured from the normal to the boundary surface. When nβ > nβ (denser medium), the light bends toward the normal and ΞΈβ < ΞΈβ.
When light travels from a denser medium to a less dense one (e.g., glass to air), there is a critical angle beyond which all light is reflected back β none is transmitted. This is total internal reflection. The critical angle is given by ΞΈ_c = arcsin(nβ Γ· nβ). Optical fibers use total internal reflection to transmit light signals over long distances with minimal loss.
Light bends because its speed changes as it enters a new medium. The refractive index n = c/v, where c is the speed of light in vacuum and v is the speed in the medium. When light slows down entering a denser medium, the wavefront changes direction to maintain continuity β this bending is refraction.
The refractive index (n) of a medium is the ratio of the speed of light in vacuum to the speed of light in that medium: n = c Γ· v. It has no units and is always β₯ 1. A higher refractive index means light travels more slowly in that medium. Diamond's high refractive index (2.417) is responsible for its exceptional brilliance.
Total internal reflection is used in optical fibers (telecommunications and internet cables), endoscopes for medical imaging, binoculars and periscopes (using prisms), retroreflectors, and diamond cutting (maximizing brilliance). It occurs when light hits a boundary at an angle greater than the critical angle while traveling in the denser medium.
No β only the speed and wavelength change when light enters a new medium. The frequency stays constant. Since color is determined by frequency, light doesn't change color when refracted. However, different frequencies refract by slightly different amounts (dispersion), which is why a prism splits white light into a rainbow spectrum.