Refraction Index Calculator

Refraction is the bending of light (or any wave) as it passes from one medium to another. This happens because light travels at different speeds in different materials. The refractive index (n) of a material describes how much slower light travels in that material compared to in a vacuum.

Refractive index formula: n = c / v

Where c is the speed of light in a vacuum (3 × 10⁸ m/s) and v is the speed of light in the material.

Snell’s Law describes the angle of refraction: n₁ × sin(θ₁) = n₂ × sin(θ₂)

Where:

• n₁ = refractive index of the first medium
• θ₁ = angle of incidence (measured from the normal — the perpendicular to the surface)
• n₂ = refractive index of the second medium
• θ₂ = angle of refraction

Common refractive indices:

• Vacuum: 1.0000 (exactly)
• Air: 1.0003 (effectively 1.0)
• Water: 1.333
• Glass (crown): 1.520
• Glass (flint): 1.620
• Diamond: 2.417
• Ice: 1.309
• Acrylic (PMMA): 1.490
• Sapphire: 1.762
• Glycerol: 1.473
• Ethanol: 1.361
• Olive oil: 1.467

Critical angle: When light travels from a denser medium to a less dense medium (e.g., glass to air), there is an angle at which the refracted ray runs along the surface (90°). Above this angle, no light escapes — this is called total internal reflection. It is the principle behind optical fibre communications. The critical angle θ_c = arcsin(n₂/n₁).

Everyday examples of refraction:

• A straw appearing bent in a glass of water
• Rainbows (different colours refract at slightly different angles through water droplets)
• Camera lenses and eyeglasses focusing light
• Mirages on hot roads (refraction through air layers of different temperatures)
• Optical fibres carrying data as light