Compute the angle of refraction, critical angle, and visualize light bending at the interface between two optical media. Based on Willebrord Snellius' law – essential for optics, lens design, and understanding mirages or fiber optics.
Snell's Law (also known as Descartes' law) governs how light rays bend when crossing the interface between two media with different refractive indices. The refraction angle θ₂ is given by: n₁ sin θ₁ = n₂ sin θ₂. This calculator solves for θ₂, determines the critical angle for total internal reflection, and provides an interactive ray diagram to visualize the bending.
When light passes from a medium with refractive index n₁ into a medium with n₂, the change in wave speed causes the ray to change direction. If n₂ > n₁ (e.g., air to water), light bends toward the normal; if n₂ < n₁ (e.g., water to air), light bends away from the normal. The critical angle exists only when n₁ > n₂, beyond which total internal reflection occurs — the principle behind fiber optics.
In modern fiber optics, light is guided through a glass core (n₁≈1.48) surrounded by a cladding (n₂≈1.46). By ensuring the incident angle exceeds the critical angle (≈80.5° from normal), total internal reflection traps light inside the core, enabling high-speed data transmission across oceans. Our calculator instantly finds the critical angle and checks for TIR conditions.
Lens designers use Snell's Law to compute how much incoming light bends at each lens surface. By controlling refraction angles, corrective lenses focus light precisely onto the retina. This tool helps verify basic refraction parameters before advanced ray tracing.
| Material | Refractive Index (n) | Typical use |
|---|---|---|
| Vacuum | 1.00000 | Reference standard |
| Air (STP) | 1.0003 | Atmospheric optics |
| Water (20°C) | 1.333 | Underwater imaging |
| Crown Glass | 1.52 | Lenses, windows |
| Flint Glass | 1.62 | Prisms |
| Diamond | 2.42 | Brilliance, dispersion |
| Optical Fiber Core | 1.46 - 1.48 | Telecom |
When light travels from a denser medium (higher n) to a rarer medium (lower n), the angle of refraction reaches 90° at the critical angle θc = arcsin(n₂/n₁). For incident angles greater than θc, all light reflects back into the first medium — this is exploited in endoscopes, binoculars, and optical sensors. Our tool marks TIR and displays the reflected ray on the diagram.
Willebrord Snellius (1580–1626) discovered the law of refraction experimentally in 1621, but René Descartes first published it in his “Dioptrique” (1637). Today, Snell's law is fundamental to lens design, seismology (wave refraction), and even underwater acoustics. The interactive diagram above visualizes the geometric intuition that helped shape modern optics.