🔦 Snell's Law Calculator
Refraction at boundaries: n₁·sinθ₁ = n₂·sinθ₂
Refracted angle θ₂
How to Use This Calculator
Pick the two media (or enter custom indices), set the incident angle from the normal, and get the refracted angle plus critical-angle and reflection analysis.
Select medium 1 (where light starts) and medium 2 (where it goes).
Enter the incident angle θ₁ in degrees, measured from the normal.
Read θ₂, the critical angle, and whether total internal reflection occurs.
The Formula
If sin θ₂ would exceed 1, refraction is impossible: that is total internal reflection, and the critical angle θc marks its onset.
Worked Example
Air (n₁ = 1.0003) to water (n₂ = 1.33), θ₁ = 30°. sin θ₂ = 1.0003 × sin 30° / 1.33 = 0.3761, so θ₂ = 22.1°. Light bends toward the normal entering water.
Optics in the Wild
Camera lenses stack elements to tame refraction, fiber optics pipe light for kilometers via total internal reflection, and a diamond's fire comes from its huge index (2.42) trapping light until precisely cut facets release it.
Common Mistakes to Avoid
Angles are measured from the NORMAL, not the surface; 30° from the surface is 60° from the normal. When going from dense to rare medium, check for total internal reflection before trusting a refracted angle. Refractive index depends on wavelength: the tabulated values are usually for yellow sodium light. For birefringent crystals like calcite, a single n does not exist.
Mirages are Snell's law in the sky: hot air near pavement has lower n, bending light upward so the road appears wet. Underwater photographers fight refraction at the mask lens, and astronomers correct for atmospheric refraction that lifts stars about half a degree near the horizon.
Total Internal Reflection in Technology
Fiber optic cables are applied Snell's law: light entering the fiber core at a shallow enough angle reflects totally at the cladding boundary, traveling kilometers with minimal loss. The internet's backbone is trillions of such reflections per second. Endoscopes use the same principle to carry images out of the human body.
Diamonds sparkle because their high refractive index (2.42) gives a tiny critical angle of about 24 degrees; skilled cutting traps light inside until it exits toward the viewer. Mirages are Snell's law in air: hot road surfaces create a gradient of refractive index that bends skylight upward by total internal reflection. Reflectors on bicycles and road signs use corner-cube geometry for the same guaranteed return.
Frequently Asked Questions
What is Snell's law?
n₁sinθ₁ = n₂sinθ₂ relates the angles of light on either side of a boundary to the refractive indices. Light bends toward the normal entering a denser medium and away leaving it. Angles are measured from the normal, not the surface.
What is refractive index?
The ratio of light speed in vacuum to speed in the material (n = c/v). Air ≈ 1.00, water 1.33, glass 1.5, diamond 2.42. Higher n means slower light and stronger bending.
What is total internal reflection?
When light tries to leave a dense medium above the critical angle θc = arcsin(n₂/n₁), no refraction is possible and all light reflects. Fiber optics, prisms, and sparkling diamonds all exploit this.
Why does a straw look bent in water?
Rays from the submerged straw refract at the water-air boundary, so your brain projects them back along straight lines to a shallower apparent position. The calculator shows the exact angle shift.
Does color affect refraction?
Yes: refractive index varies slightly with wavelength (dispersion). Blue bends more than red, which is how prisms split white light into rainbows and why camera lenses need achromatic correction.