Optical constants

Refractive index of Air

Ciddor 1996: n 0.23–1.690 µm

Data: formula 6
Range: 0.23–1.69 µm
Temperature: 288.15 K
Licence: CC0-1.0

Axis Log x Log y

Click the plot to set the calculator wavelength.

At one wavelength

Refractive index n: 1.00028
Extinction coefficient k: 0

Permittivity ε₁: 1.00055
Permittivity ε₂: 0

Absorption coefficient α: 0 cm⁻¹
Penetration depth δ = λ/(2πk): — nm

Abbe number V_d: 89.301
Chromatic dispersion dn/dλ: -1.59084e-05 µm⁻¹

Group index n_g: 1.00029
Group velocity dispersion: 0.0302171 fs²/mm

Dispersion parameter D: -0.164851 ps/(nm·km)
Photon energy: 2.11001 eV

ε = (n + ik)², α = 4πk/λ, n_g = n − λ dn/dλ, GVD = λ³/(2πc²) d²n/dλ², D = −(λ/c) d²n/dλ². Group-velocity dispersion is given for formula data only.

Use it in Lightsmith

Load this data in Python, simulate in one more line

pip install lightsmith

import lightsmith as ls

# Air: Ciddor 1996: n 0.23–1.690 µm
air = ls.fetch_refractiveindex("other", "air", "Ciddor", ref="c5c2f188e848453def5970e347399d653df2ffc2")
print(air.range_nm)  # (230, 1690) nm
eps = air.eps([633])  # complex permittivity

Downloads the original record once (pinned to the imported snapshot) and caches it.

import json, urllib.request
import lightsmith as ls

url = "https://materials.lightsmith.dev/v1/datasets/ds_6dd461dd74b9/lightsmith"
air = ls.Tabulated.model_validate(json.load(urllib.request.urlopen(url)))
print(air.source)  # citation and provenance travel with the data

Any dataset here, as the library's Tabulated material (air/ciddor-1996).

# ... load air as above, then:
sim = ls.Simulation(
    particles=[ls.Particle(shape=ls.Sphere(radius_nm=50), material=air)],
    medium_index=1.0,
    wavelengths=ls.WavelengthRange(start_nm=400, stop_nm=1000, num=81),
)
res = ls.solve(sim)  # exact Mie for a sphere
print(res.q_ext)     # extinction efficiency at each wavelength

Same spec runs with DDA, FDTD, BEM or T-matrix: ls.compare(sim, ["mie", "dda"]).

Materials guide Open a sphere of it in Studio Quick start Ask the community

Lightsmith is open source (MIT): Mie, T-matrix, BEM, DDA, FDTD, RCWA, TMM, mode solvers and inverse design behind one spec, on CPU or GPU. GitHub.

Dispersion formula

Gases (formula 6), λ in µm

n - 1 = \frac{0.05792105}{238.0185 - λ^{−2}} + \frac{0.00167917}{57.362 - λ^{−2}}

Valid from 0.23 to 1.69 µm.

Coefficients as stored

C_i	Value
C1	0.0
C2	0.05792105
C3	238.0185
C4	0.00167917
C5	57.362

Comments and conditions

Standard air: dry air at 15 °C, 101.325 kPa and with 450 ppm CO₂ content.

Conditions

temperature: 288.15 K
pressure: 101325

References

P. E. Ciddor. Refractive index of air: new equations for the visible and near infrared. Appl. Optics 35, 1566-1573 (1996)
[Calculation script (Python) - can be used to calculate the refractive index of air for specific values of humidity, temperature, pressure, and CO₂ concentration]

doi:10.1364/ao.35.001566 Refractive index of air: new equations for the visible and near infrared, Applied Optics (1996)

Cite

Philip E. Ciddor. Refractive index of air: new equations for the visible and near infrared. Applied Optics, 35, 1566 (1996), doi:10.1364/ao.35.001566; [Calculation script (Python) - can be used to calculate the refractive index of air for specific values of humidity, temperature, pressure, and CO2 concentration]; Data from the refractiveindex.info database (M. N. Polyanskiy, Sci. Data 11, 94 (2024), doi:10.1038/s41597-023-02898-2)

Data

Computed on 400 wavelengths, the same grid as the API and the library

CSV comma separated TXT tab separated YAML n, k Full database record original YAML All quantities CSV JSON metadata

Air, Ciddor 1996: n 0.23–1.690 µm: n and k versus wavelength
λ (µm)	n
0.23	1.000308
0.231153	1.000308
0.232311	1.000307
0.233475	1.000307
0.234645	1.000306
0.235821	1.000306
0.237002	1.000305
0.23819	1.000305
0.239384	1.000305
0.240583	1.000304
0.241789	1.000304
0.243	1.000304
0.244218	1.000303
0.245442	1.000303
0.246672	1.000302
0.247908	1.000302
0.24915	1.000302
0.250399	1.000301
0.251653	1.000301
0.252914	1.000301
0.254182	1.0003
0.255455	1.0003
0.256736	1.0003
0.258022	1.000299
0.259315	1.000299
0.260614	1.000299
0.26192	1.000298
0.263233	1.000298
0.264552	1.000298
0.265878	1.000298
0.26721	1.000297
0.268549	1.000297
0.269895	1.000297
0.271247	1.000296
0.272606	1.000296
0.273972	1.000296
0.275345	1.000296
0.276725	1.000295
0.278112	1.000295
0.279505	1.000295
0.280906	1.000295
0.282313	1.000294
0.283728	1.000294
0.28515	1.000294
0.286579	1.000294
0.288015	1.000293
0.289458	1.000293
0.290909	1.000293
0.292366	1.000293
0.293831	1.000292
0.295304	1.000292
0.296784	1.000292
0.298271	1.000292
0.299765	1.000292
0.301268	1.000291
0.302777	1.000291
0.304294	1.000291
0.305819	1.000291
0.307352	1.000291
0.308892	1.00029
0.31044	1.00029
0.311995	1.00029
0.313559	1.00029
0.31513	1.00029
0.316709	1.000289
0.318296	1.000289
0.319891	1.000289
0.321494	1.000289
0.323105	1.000289
0.324724	1.000289
0.326351	1.000288
0.327987	1.000288
0.32963	1.000288
0.331282	1.000288
0.332942	1.000288
0.334611	1.000288
0.336287	1.000287
0.337972	1.000287
0.339666	1.000287
0.341368	1.000287
0.343079	1.000287
0.344798	1.000287
0.346526	1.000286
0.348262	1.000286
0.350007	1.000286
0.351761	1.000286
0.353524	1.000286
0.355295	1.000286
0.357076	1.000286
0.358865	1.000285
0.360663	1.000285
0.362471	1.000285
0.364287	1.000285
0.366112	1.000285
0.367947	1.000285
0.369791	1.000285
0.371644	1.000284
0.373506	1.000284
0.375378	1.000284
0.377259	1.000284
0.379149	1.000284
0.381049	1.000284
0.382959	1.000284
0.384878	1.000284
0.386806	1.000284
0.388745	1.000283
0.390693	1.000283
0.39265	1.000283
0.394618	1.000283
0.396595	1.000283
0.398583	1.000283
0.40058	1.000283
0.402587	1.000283
0.404605	1.000283
0.406632	1.000282
0.40867	1.000282
0.410718	1.000282
0.412776	1.000282
0.414844	1.000282
0.416923	1.000282
0.419012	1.000282
0.421112	1.000282
0.423222	1.000282
0.425343	1.000282
0.427474	1.000281
0.429616	1.000281
0.431769	1.000281
0.433933	1.000281
0.436107	1.000281
0.438293	1.000281
0.440489	1.000281
0.442696	1.000281
0.444915	1.000281
0.447144	1.000281
0.449385	1.000281
0.451637	1.00028
0.4539	1.00028
0.456174	1.00028
0.45846	1.00028
0.460757	1.00028
0.463066	1.00028
0.465387	1.00028
0.467719	1.00028
0.470063	1.00028
0.472418	1.00028
0.474785	1.00028
0.477165	1.00028
0.479556	1.00028
0.481959	1.000279
0.484374	1.000279
0.486801	1.000279
0.48924	1.000279
0.491692	1.000279
0.494156	1.000279
0.496632	1.000279
0.499121	1.000279
0.501622	1.000279
0.504135	1.000279
0.506662	1.000279
0.509201	1.000279
0.511752	1.000279
0.514317	1.000279
0.516894	1.000279
0.519484	1.000278
0.522087	1.000278
0.524703	1.000278
0.527333	1.000278
0.529975	1.000278
0.532631	1.000278
0.5353	1.000278
0.537982	1.000278
0.540678	1.000278
0.543387	1.000278
0.54611	1.000278
0.548847	1.000278
0.551597	1.000278
0.554361	1.000278
0.557139	1.000278
0.559931	1.000278
0.562737	1.000278
0.565557	1.000278
0.568391	1.000277
0.571239	1.000277
0.574101	1.000277
0.576978	1.000277
0.57987	1.000277
0.582775	1.000277
0.585696	1.000277
0.588631	1.000277
0.59158	1.000277
0.594545	1.000277
0.597524	1.000277
0.600518	1.000277
0.603527	1.000277
0.606552	1.000277
0.609591	1.000277
0.612646	1.000277
0.615716	1.000277
0.618801	1.000277
0.621902	1.000277
0.625018	1.000277
0.62815	1.000277
0.631298	1.000277
0.634461	1.000277
0.637641	1.000276
0.640836	1.000276
0.644047	1.000276
0.647274	1.000276
0.650518	1.000276
0.653778	1.000276
0.657054	1.000276
0.660346	1.000276
0.663655	1.000276
0.666981	1.000276
0.670323	1.000276
0.673682	1.000276
0.677058	1.000276
0.680451	1.000276
0.68386	1.000276
0.687287	1.000276
0.690731	1.000276
0.694193	1.000276
0.697671	1.000276
0.701167	1.000276
0.704681	1.000276
0.708212	1.000276
0.711761	1.000276
0.715328	1.000276
0.718912	1.000276
0.722515	1.000276
0.726135	1.000276
0.729774	1.000276
0.733431	1.000276
0.737106	1.000275
0.7408	1.000275
0.744512	1.000275
0.748242	1.000275
0.751992	1.000275
0.75576	1.000275
0.759547	1.000275
0.763353	1.000275
0.767179	1.000275
0.771023	1.000275
0.774887	1.000275
0.77877	1.000275
0.782672	1.000275
0.786594	1.000275
0.790536	1.000275
0.794497	1.000275
0.798478	1.000275
0.802479	1.000275
0.806501	1.000275
0.810542	1.000275
0.814604	1.000275
0.818686	1.000275
0.822788	1.000275
0.826911	1.000275
0.831055	1.000275
0.835219	1.000275
0.839405	1.000275
0.843611	1.000275
0.847838	1.000275
0.852087	1.000275
0.856357	1.000275
0.860648	1.000275
0.86496	1.000275
0.869295	1.000275
0.873651	1.000275
0.878029	1.000275
0.882429	1.000275
0.88685	1.000275
0.891294	1.000275
0.895761	1.000275
0.900249	1.000275
0.904761	1.000275
0.909294	1.000274
0.913851	1.000274
0.91843	1.000274
0.923032	1.000274
0.927658	1.000274
0.932306	1.000274
0.936978	1.000274
0.941673	1.000274
0.946392	1.000274
0.951134	1.000274
0.955901	1.000274
0.960691	1.000274
0.965505	1.000274
0.970343	1.000274
0.975205	1.000274
0.980092	1.000274
0.985003	1.000274
0.989939	1.000274
0.9949	1.000274
0.999885	1.000274
1.0049	1.000274
1.00993	1.000274
1.01499	1.000274
1.02008	1.000274
1.02519	1.000274
1.03033	1.000274
1.03549	1.000274
1.04068	1.000274
1.04589	1.000274
1.05113	1.000274
1.0564	1.000274
1.0617	1.000274
1.06702	1.000274
1.07236	1.000274
1.07774	1.000274
1.08314	1.000274
1.08856	1.000274
1.09402	1.000274
1.0995	1.000274
1.10501	1.000274
1.11055	1.000274
1.11611	1.000274
1.12171	1.000274
1.12733	1.000274
1.13298	1.000274
1.13865	1.000274
1.14436	1.000274
1.15009	1.000274
1.15586	1.000274
1.16165	1.000274
1.16747	1.000274
1.17332	1.000274
1.1792	1.000274
1.18511	1.000274
1.19105	1.000274
1.19702	1.000274
1.20301	1.000274
1.20904	1.000274
1.2151	1.000274
1.22119	1.000274
1.22731	1.000274
1.23346	1.000274
1.23964	1.000274
1.24585	1.000274
1.25209	1.000274
1.25837	1.000274
1.26467	1.000274
1.27101	1.000274
1.27738	1.000274
1.28378	1.000274
1.29022	1.000274
1.29668	1.000274
1.30318	1.000274
1.30971	1.000274
1.31627	1.000274
1.32287	1.000274
1.3295	1.000273
1.33616	1.000273
1.34285	1.000273
1.34958	1.000273
1.35635	1.000273
1.36314	1.000273
1.36997	1.000273
1.37684	1.000273
1.38374	1.000273
1.39067	1.000273
1.39764	1.000273
1.40464	1.000273
1.41168	1.000273
1.41876	1.000273
1.42587	1.000273
1.43301	1.000273
1.44019	1.000273
1.44741	1.000273
1.45466	1.000273
1.46195	1.000273
1.46928	1.000273
1.47664	1.000273
1.48404	1.000273
1.49148	1.000273
1.49895	1.000273
1.50646	1.000273
1.51401	1.000273
1.5216	1.000273
1.52922	1.000273
1.53688	1.000273
1.54459	1.000273
1.55233	1.000273
1.5601	1.000273
1.56792	1.000273
1.57578	1.000273
1.58367	1.000273
1.59161	1.000273
1.59959	1.000273
1.6076	1.000273
1.61566	1.000273
1.62375	1.000273
1.63189	1.000273
1.64007	1.000273
1.64829	1.000273
1.65655	1.000273
1.66485	1.000273
1.67319	1.000273
1.68157	1.000273
1.69	1.000273

Optical transmission calculator

Free-standing sample in vacuum, normal incidence

Transmittance T: —
Reflectance R: —

Fresnel reflection calculator

R_p: —
R_s: —
R = (R_p+R_s)/2: —
Phase φ_p: —
Phase φ_s: —
Brewster angle θ_B: —
Critical angle θ_C: —

Air: all datasets

About Air

Air is a mixture of gases that constitutes the Earth's atmosphere and is vital for most forms of life on our planet. It primarily consists of nitrogen (approximately 78%) and oxygen (about 21%), with small amounts of other gases such as argon, carbon dioxide, neon, helium, and methane. The exact composition can vary depending on location and environmental conditions. Air is colorless, odorless, and tasteless. From a physical perspective, air plays a crucial role in many processes such as weather patterns, the water cycle, and is also an important medium for sound transmission. In terms of its optical properties, air has a refractive index very close to 1 (approximately 1.0003 at sea level under standard conditions), which varies slightly with temperature, humidity, and pressure. This refractive index is crucial in various applications ranging from astronomical observations to the design of optical systems where light travels through the atmosphere. Understanding the properties of air, including its refractive index, is essential for disciplines such as meteorology, environmental science, aviation, and optical engineering.

More about Air →

Provenance

Version: 1 (snapshot c5c2f18)
Source page: refractiveindex.info
Original file: database/data/other/mixed gases/air/nk/Ciddor.yml
ID: ds_6dd461dd74b9
API: /v1/datasets/ds_6dd461dd74b9

Plot