Snell's Law
Calculate the angle of refraction using Snell's Law n₁ sin θ₁ = n₂ sin θ₂. Free online calculator with refractive index presets for air, water, glass, and diamond.
About This Calculator
Snell's Law Calculator computes the angle of refraction when light passes from one medium to another using the fundamental law of refraction: n₁ sin θ₁ = n₂ sin θ₂. Whether you are a physics student studying optics, an engineer designing optical systems, or a professional working with fiber optics or lens design, this tool provides instant, accurate results with refractive index presets for common media including air, water, glass, acrylic, and diamond.
The calculator uses the full Snell's Law equation: θ₂ = arcsin(n₁ sin θ₁ / n₂). If the light travels from a denser to a rarer medium and the angle of incidence exceeds the critical angle, the tool correctly reports total internal reflection (TIR) — the phenomenon that makes fiber optics and prism-based reflection possible. The critical angle itself is calculated as θ_c = arcsin(n₂ / n₁) when n₁ > n₂. Results include a detailed breakdown table showing incidence angle, refraction angle, refractive indices, and critical angle where applicable, plus interactive bar and pie charts for visual analysis.
Snell's Law, discovered by the Dutch mathematician Willebrord Snellius in 1621, is one of the fundamental principles of optics. It applies not only to visible light but to all electromagnetic waves and even sound waves crossing boundaries between different media. The refractive index of a medium — the ratio of the speed of light in vacuum to its speed in that medium — determines how much the light bends. Higher refractive indices (like diamond at 2.417) slow light more and cause greater bending, while lower values (like air at 1.000293) have minimal effect on the light's path.
Frequently Asked Questions
What is Snell's Law of refraction?
Snell's Law, also known as the law of refraction, describes how light bends when passing from one medium to another. The formula is n₁ sin θ₁ = n₂ sin θ₂, where n₁ and n₂ are the refractive indices of the two media, and θ₁ and θ₂ are the angles of incidence and refraction measured from the normal to the boundary.
How do I calculate the angle of refraction?
To find the angle of refraction, use Snell's Law: θ₂ = arcsin(n₁ sin θ₁ / n₂). Enter the refractive indices of both media and the angle of incidence, then click Calculate. The tool automatically computes the refracted angle and alerts you when total internal reflection occurs.
What is total internal reflection?
Total internal reflection occurs when light travels from a denser medium (higher refractive index) to a rarer medium (lower refractive index) at an angle greater than the critical angle. When this happens, all light is reflected back into the first medium instead of passing through — this phenomenon is used in fiber optics and prisms.
What is the critical angle in Snell's Law?
The critical angle is the angle of incidence at which the refracted ray travels along the boundary between two media (angle of refraction = 90°). It is calculated as θ_c = arcsin(n₂ / n₁) where n₁ > n₂. For example, the critical angle from water (n=1.333) to air (n=1) is approximately 48.75°.
What are common refractive indices?
Common refractive indices include: Air — 1.000293, Water at 20°C — 1.333, Ethanol — 1.361, Ice — 1.309, Window Glass — 1.52, Acrylic — 1.49, and Diamond — 2.417. Vacuum has a refractive index of exactly 1.0 by definition.
Does Snell's Law apply to all types of waves?
Yes, Snell's Law applies to any wave passing through an interface between two isotropic media, including sound waves and seismic waves. It is derived from the principle of wavefront continuity and wave velocity changes, making it universal for wave refraction in all phases of matter.
What happens when light goes from air to water?
When light travels from air (n≈1) to water (n≈1.333), it bends toward the normal. For a 30° angle of incidence, the angle of refraction is approximately 22.1°. This is why objects underwater appear shifted from their actual position — the light rays bend as they enter the water.
Why is Snell's Law important in real-world applications?
Snell's Law is essential for designing lenses in cameras and eyeglasses, fiber optic communications where total internal reflection guides light, prism-based spectroscopy, underwater optics, and medical imaging devices like endoscopes that use light refraction for internal visualization.