🔺 Snell's Law Calculator (Refraction)
Find the angle of refraction as light crosses between media (Snell’s law), with critical-angle and total-internal-reflection detection.
Angle of refraction θ₂
19.471°
Ray bends toward the normal (into denser medium).
Snell’s law: n₁·sin θ₁ = n₂·sin θ₂. Critical angle θc = arcsin(n₂/n₁) when n₁ > n₂. 🔒 Computed in your browser.
How the snell's law calculator (refraction) works
Snell’s law relates the angles and refractive indices at a boundary: n₁·sin θ₁ = n₂·sin θ₂. Enter the two indices and the incidence angle and the tool gives the refraction angle, tells you whether the ray bends toward or away from the normal, and, when passing to a less dense medium, the critical angle and whether total internal reflection occurs. The refractive index n = c/v measures how much light slows in a medium; a higher index bends light more strongly toward the normal.
The critical-angle and total-internal-reflection verdict is the differentiator (and an AI stumbling point). Use the built-in indices (air 1.00, water 1.33, glass 1.50, diamond 2.42) or type your own.
Frequently asked questions
What is Snell’s law?
It governs refraction: n₁·sin θ₁ = n₂·sin θ₂, where n is the refractive index and θ the angle from the normal. Light bends toward the normal entering a denser medium and away entering a rarer one.
How do I find the angle of refraction?
Rearrange to sin θ₂ = (n₁/n₂)·sin θ₁, then take the inverse sine. The tool does this and shows θ₂ directly.
What is the critical angle?
The incidence angle (going from a denser to a rarer medium) beyond which light can no longer refract out: θc = arcsin(n₂/n₁). Above it, total internal reflection occurs.
What is total internal reflection?
When light hits a boundary to a less dense medium beyond the critical angle, none refracts. It all reflects back inside. It’s how optical fibres guide light.
What refractive index should I use?
Air ≈ 1.00, water 1.33, typical glass 1.50, diamond 2.42. You can enter any value for your specific material.
Worked example: air to water
Light hitting water (n = 1.33) from air (n = 1.00) at 30°: sin θ₂ = (1.00/1.33)·sin 30° = 0.376, so θ₂ = arcsin(0.376) ≈ 22°. The ray bends toward the normal entering the denser water.
What is the critical angle for water?
Going from water (n = 1.33) to air (n = 1.00), θc = arcsin(1.00/1.33) ≈ 48.8°. Beyond that incidence angle light undergoes total internal reflection instead of refracting out.
What is the refractive index?
n = c/v, the ratio of the speed of light in a vacuum to its speed in the medium. A higher index means light travels slower and bends more; for ordinary materials it is always at least 1.
Does refraction change the wavelength or the frequency?
The frequency stays the same when light crosses a boundary, but the speed and wavelength both change (λ = v/f). That change in speed is what bends the ray, as Snell’s law describes.