Waves & Optics
Snell's Law Calculator
Calculate refraction angle, critical angle for TIR, and look up refractive indices for common materials.
Result
n₁sinθ₁ = n₂sinθ₂
Critical Angle
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TIR Status
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Step-by-Step Solution
What is Snell's Law?
Snell's Law describes how light (or any wave) bends when it crosses the boundary between two media with different refractive indices. It governs everything from how a straw appears bent in water to how optical fibres transmit data around the globe.
n₁sinθ₁ = n₂sinθ₂
n₁, n₂ = refractive indices | θ₁ = angle of incidence | θ₂ = angle of refraction
💡 When light moves from a denser medium (high n) to a less dense medium (low n) at an angle greater than the critical angle, it undergoes Total Internal Reflection (TIR) — the principle behind optical fibres.
Real-World Applications
Lenses & Glasses
All lenses work by refracting light according to Snell's Law to focus or diverge rays.
Optical Fibres
TIR keeps light bouncing inside the fibre core, enabling global internet communication.
Water Illusions
A straw appears bent in water because light changes direction at the water-air boundary.
Gem Cutting
Diamonds are cut at precise angles to maximise TIR and make light sparkle inside.
Frequently Asked Questions
What is total internal reflection?
TIR occurs when light in a denser medium hits the boundary at an angle greater than the critical angle. Instead of refracting out, all the light reflects back inside. The critical angle is given by: sin(θ_c) = n₂/n₁.
What is the refractive index?
The refractive index n = c/v, where c is the speed of light in vacuum and v is the speed in the medium. Water has n = 1.333 (light travels 25% slower). Diamond has n = 2.42 (light is less than half speed in vacuum).
Why do diamonds sparkle so much?
Diamond has a very high refractive index (2.42) and a low critical angle (~24°). Most light entering the diamond undergoes TIR multiple times before exiting, creating the characteristic sparkle.