Snell's Law / Refraction Calculator

Snell's law (also called the law of refraction) describes how light bends when it passes from one transparent medium into another. It relates the angle of incidence (θ₁) and angle of refraction (θ₂), both measured from the normal (the line perpendicular to the surface), to the refractive indices of the two media: n₁ sin(θ₁) = n₂ sin(θ₂). The refractive index n of a medium is the ratio of the speed of light in vacuum (c) to its speed in that medium (v), so n = c / v. When light enters a denser medium (higher n) it bends toward the normal; when it enters a rarer medium (lower n) it bends away from the normal. Our Snell's law calculator applies this relationship and also computes the critical angle and total internal reflection.

1. Select What to Solve For:Choose "Angle of Refraction" to find θ₂ from the angle of incidence, or "Angle of Incidence" to work backward from a known refraction angle. The refraction calculator handles both solve modes with the same interface.
2. Choose the Two Media: Pick from 10 optical medium presets — vacuum, air, water, glass, diamond, and more — or enter a custom refractive index for either side. The Snell's law calculator uses standard refractive indices measured at the sodium-D wavelength (≈589 nm).
3. Read the Full Result: The refraction calculator displays the angle of refraction (or incidence), the critical angle, whether total internal reflection occurs, the deviation angle, and the speed of light in each medium — all alongside a live ray diagram. Every calculation runs locally in your browser.

• Angle of Refraction (θ₂): The angle the transmitted ray makes with the normal, found from θ₂ = arcsin( n₁ sin θ₁ / n₂ ). This is the primary output of the Snell's law calculator when solving from the incidence angle.
• Critical Angle (θc):The angle of incidence beyond which total internal reflection occurs. It exists only when n₁ > n₂ and is calculated as θc = arcsin( n₂ / n₁ ). For a water-to-air boundary, θc ≈ 48.6°.
• Total Internal Reflection (TIR): When light travels from a denser to a rarer medium and the incidence angle exceeds the critical angle, no light is transmitted — it is entirely reflected. The refraction calculator flags this case and shows the reflected ray on the diagram.
• Speed of Light in Each Medium: Using v = c / n, the calculator shows how fast light travels in both media. In diamond (n = 2.417), light slows to about 1.24 × 10⁸ m/s — less than half its vacuum speed.

The Snell's law calculator assumes flat, smooth interfaces and monochromatic light at the sodium-D wavelength (≈589 nm). Because refractive index varies slightly with wavelength — an effect called dispersion — the angle of refraction differs for different colours, which is why prisms split white light into a spectrum. The preset indices are typical room-temperature values; real-world materials can vary with temperature, pressure, and purity. Angles are measured from the normal, not the surface, and must be between 0° and 90°. Total internal reflection only occurs when light moves from a higher-index medium to a lower-index one.