Refractive Index Calculator
Find refractive index from light speed in a medium, or from Snell's law at an interface. n=c/v. Water n≈1.333; glass≈1.5; diamond≈2.42.
Input Data
Results
At a glance:Refractive index n=c/v is the ratio of the vacuum speed of light to its speed in a medium. From Snell's law, n₁sinθ₁=n₂sinθ₂, so relative index equals the inverse ratio of the sines. Properties: (1) n≥1 for ordinary media; (2) higher n means slower light and stronger bending; (3) n varies with wavelength (dispersion). Applications: (1) lens and prism design; (2) gemstone identification (diamond n≈2.42); (3) anti-reflection and optical coatings; (4) fibre and waveguide design; (5) atmospheric refraction.
Formula
Definition: n = c/v
Snell's law: n₁·sinθ₁ = n₂·sinθ₂
Relative index: n₂/n₁ = sinθ₁/sinθ₂
$$n = \frac{c}{v}, \quad n_1 \sin\theta_1 = n_2 \sin\theta_2$$How to Use
- Speed mode: enter light speed in the medium to get n=c/v.
- Snell mode: enter n₁, θ₁ and θ₂ to solve for n₂.
- Both modes return the refractive index consistently.
Case Studies
Diamond versus glass
Diamond n≈2.42 bends light far more than glass (n≈1.5), giving its brilliance and fire through total internal reflection.
A gem tester compares n and dispersion; glass imitations show lower n.
Water n≈1.333 explains why a submerged object looks shallower than it is.
Content review: Calculatorism Science Team. Results are for reference only; please refer to the relevant authorities for the official figures.