Refractive Index Calculator

Calculate refractive index, light speed in medium, or wavelength using n = c/v = λ₀/λ.

🔭 Optics📐 n = c/v💡 Refraction
Speed of light in medium (v) m/s
⚠️ Enter valid positive numbers.

What Is Refractive Index?

The refractive index n of a medium is the ratio of the speed of light in vacuum to the speed in the medium: n = c/v, where c = 2.998×10⁸ m/s and v is the phase velocity of light in the medium. Higher n means slower light and more bending at interfaces (Snell's Law: n₁sinθ₁ = n₂sinθ₂).

The refractive index also equals the ratio of wavelengths: n = λ₀/λ_medium. When light enters a denser medium, its wavelength decreases and speed decreases, but frequency stays constant (f = c/λ₀ = v/λ_medium). The color of light depends on frequency, which is unchanged by the medium.

n varies with wavelength — a phenomenon called dispersion. Crown glass: n_blue = 1.524, n_red = 1.514. This difference (0.01) causes prisms to separate white light into spectra and causes chromatic aberration in lenses. Abbe number V = (n_yellow − 1)/(n_blue − n_red) characterizes dispersion — higher V = less dispersion.

Absolute refractive index n relates to permittivity ε and permeability μ: n = √(εᵣμᵣ). For most optical materials: μᵣ ≈ 1, so n ≈ √εᵣ. Metamaterials with negative εᵣ and μᵣ can have negative n — enabling 'superlenses' and cloaking devices.

Formula Reference Table

Solve ForFormulaNotes
Refractive indexn = c/vc = 2.998×10⁸ m/s
Speed in mediumv = c/nm/s
Wavelength in mediumλ = λ₀/nλ₀ = vacuum wavelength
Snell's law connectionn₁sin θ₁ = n₂sin θ₂Light bends at interfaces
Critical angleθ_c = arcsin(n₂/n₁)n₁ > n₂; total internal reflection
Dispersionn = n(λ)Cauchy: n = A + B/λ²

3 Worked Examples

Example 1
Speed in Glass

n = 1.5 (crown glass). Find v.

  • v = c/n = 2.998×10⁸ / 1.5 = 1.999×10⁸ m/s
  • = 199,900 km/s (about 2/3 speed of light in vacuum)
✓ v = 2.0×10⁸ m/s in crown glass
Example 2
Wavelength in Diamond

Yellow light λ₀ = 589 nm in vacuum. n_diamond = 2.42.

  • λ = λ₀/n = 589/2.42 = 243 nm in diamond
  • The wavelength halves, but frequency stays constant at c/λ₀
✓ λ = 243 nm inside diamond (frequency unchanged)
Example 3
Find n from Speed

Light travels at v = 2.25×10⁸ m/s in an unknown medium.

  • n = c/v = 2.998×10⁸ / 2.25×10⁸ = 1.332
  • Close to n_water = 1.333 — this is water!
✓ n = 1.332 → water

Real-World Applications

👓
Optics Design
Lens designers choose glass types by n and Abbe number. High n → thinner lenses. High V → less chromatic aberration. Crown glass (n=1.52, V=60) for achromat vs flint glass (n=1.62, V=36) for chromatic control.
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Diamond Brilliance
Diamond's high n (2.42) gives θ_c = 24.4° — most light undergoes total internal reflection multiple times before exiting the top. Gem cutters maximize this with specific facet angles.
🔭
Optical Fibers
Silica fiber (n=1.46) has very low absorption at 1,550 nm. The n difference between core and cladding determines the numerical aperture and light-guiding ability.
🌈
Atmospheric Optics
Air n decreases with altitude (density decreases). This bends light from stars and planets — they appear 0.5° higher than geometrically. The 'green flash' is extreme refraction-dispersion of the setting Sun.
⚗️
Interferometry
Measuring n of gas samples by interferometry enables precise concentration measurements. The Fabry-Pérot interferometer detects path length differences ΔL = (n−1)×L with sub-nanometer precision.

Common Mistakes to Avoid

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Confusing n with v

n is dimensionless (always ≥ 1 for ordinary media). v is the light speed in the medium (m/s). n = c/v → high n = low v.

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Forgetting wavelength changes, frequency doesn't

λ_medium = λ_vacuum/n (shorter in medium). f_medium = f_vacuum (unchanged). Light's color (perceived) depends on frequency, not wavelength — so color doesn't change when light enters glass.

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Applying vacuum n = 1 to air

Air n = 1.0003, not exactly 1. For most applications negligible, but in precision interferometry or GPS signal propagation, the difference matters.

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Using n for magnetic materials

n = √(εᵣμᵣ). For optical frequencies, μᵣ ≈ 1 for natural materials, so n ≈ √εᵣ. But for microwave metamaterials, μᵣ ≠ 1 and can be negative, giving negative n.

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Not accounting for dispersion

n depends on wavelength. Using n_sodium (589 nm) for blue light (450 nm) introduces error. For precision optics, use wavelength-specific n from Sellmeier equation.

Frequently Asked Questions

What determines the refractive index? ▾
n is determined by how light interacts with the atoms in the medium. Light's oscillating electric field drives electron oscillations. Near natural resonance frequencies (UV for glass), oscillations are large, slowing and storing energy — increasing n. Far from resonances, n approaches 1. Dense, electron-rich materials generally have higher n.
What is the Sellmeier equation? ▾
n²(λ) = 1 + Σ B_i λ²/(λ²−C_i), where B_i and C_i are material constants fit to measured n(λ). Used by lens designers to accurately model dispersion across the full visible spectrum. Published for all optical glass types.
Why is diamond so brilliant? ▾
High n (2.42) gives a low critical angle (24.4°). Light entering through the top facets bounces repeatedly off internal facets via total internal reflection before exiting upward — concentrating it toward the observer's eye. Specific cut angles (brilliant cut) maximize this effect.
What is birefringence? ▾
Some crystals have different n for different polarizations (ordinary ray n_o, extraordinary ray n_e). Calcite (n_o=1.658, n_e=1.486) creates double images. Polarizing optics use birefringent crystals. Stressed glass shows birefringence — stress birefringence in photoelastic analysis reveals internal stress fields.
What are metamaterials? ▾
Artificial structures with subwavelength features engineered to have specific ε and μ at chosen frequencies. Negative ε and μ simultaneously → negative n → light bends 'backwards' at interfaces. Applications: superlenses (imaging below diffraction limit), electromagnetic cloaks, flat lenses (metalenses). Currently limited to specific frequencies and narrow bandwidths.
How does n relate to the speed of light? ▾
Nothing travels faster than c in vacuum. In media, the phase velocity v = c/n < c. But group velocity (speed of information/energy) can differ from phase velocity in dispersive media — and can be less than, equal to, or greater than c in unusual situations. Only the group velocity, not phase velocity, is constrained to < c for information transmission.
What is chromatic aberration? ▾
Different wavelengths have different n → different focal lengths for the same lens. Blue light (n higher → shorter f) focuses closer than red light → blurry color fringes. Corrected by achromatic doublets: crown (low dispersion) and flint (high dispersion) glass paired to cancel chromatic error while maintaining focusing power.
What is optical fiber NA? ▾
Numerical aperture: NA = √(n_core² − n_clad²). Light entering within angle θ_accept = arcsin(NA) undergoes total internal reflection inside. For n_core=1.46, n_clad=1.42: NA = √(2.1316−2.0164) = 0.34. Larger NA → more light collection (important for coupling between fiber and LED/laser).

Related Physics Calculators

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Formula Explorer connections

Interpretation: This relationship connects light propagation, geometry, wavelength, refraction, interference or image formation. Assumption: Use a consistent sign convention and units. Paraxial rays, thin elements, coherent light, vacuum wavelength or ideal optical components may be assumed.

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