Snell's Law Calculator
Determine the refraction angle when light passes between two media of different refractive indices using Snell's Law. Useful in optics coursework, lens design, and understanding phenomena like rainbows and fiber optics.
About this calculator
Snell's Law governs how light bends when crossing the boundary between two media: n₁ · sin(θ₁) = n₂ · sin(θ₂). Here n₁ and n₂ are the refractive indices of the first and second media, θ₁ is the angle of incidence, and θ₂ is the angle of refraction — both measured from the normal to the surface. Rearranging gives: θ₂ = arcsin((n₁ · sin(θ₁)) / n₂). When light moves from a denser to a rarer medium (n₁ > n₂), it bends away from the normal. If the argument of arcsin exceeds 1, total internal reflection occurs instead of refraction. Snell's Law is the basis for lens design, fiber optic light guiding, and natural optical effects like the apparent bending of a straw in water.
How to use
Suppose light travels from glass (n₁ = 1.5) and strikes a glass-water interface at θ₁ = 30°. The refractive index of water is n₂ = 1.33. Enter n1 = 1.5, theta1 = 30, n2 = 1.33. The calculator evaluates: θ₂ = arcsin((1.5 × sin 30°) / 1.33) = arcsin((1.5 × 0.5) / 1.33) = arcsin(0.7519) ≈ 48.75°. Light bends away from the normal as it exits the denser glass into the less dense water, which is the expected result.
Frequently asked questions
What happens when the refraction angle calculated by Snell's Law exceeds 90 degrees?
When the ratio n₁ · sin(θ₁) / n₂ is greater than 1, the arcsin function has no real solution, meaning refraction is impossible. This situation is called total internal reflection: all light is reflected back into the denser medium rather than transmitted. It only occurs when light travels from a denser medium (higher n) to a rarer one (lower n) at an angle greater than the critical angle. This principle is the foundation of fiber optic cables, which guide light over long distances with minimal loss.
How do refractive indices of common materials affect Snell's Law calculations?
The refractive index of a material indicates how much slower light travels in it compared to a vacuum (n = 1). Air has n ≈ 1.0003, water n ≈ 1.33, glass n ≈ 1.5, and diamond n ≈ 2.42. Higher refractive index means light bends more strongly at an interface. For example, light entering diamond from air bends sharply, which is why diamonds sparkle — they undergo total internal reflection many times inside before light exits. Choosing the right materials in optical system design depends heavily on controlling these bending angles.
Why is the angle in Snell's Law measured from the normal and not the surface?
The normal to a surface is the perpendicular reference line from which all angles are consistently measured in optics. Using the normal ensures the law holds universally regardless of the orientation of the surface. If angles were measured from the surface itself, a flat surface (90° from the normal) would give ambiguous results. The convention also keeps the mathematics symmetric: at normal incidence (θ₁ = 0°), sin(0) = 0, so no bending occurs, which matches physical intuition perfectly.