Wolfram Function Repository

Instant-use add-on functions for the Wolfram Language

Function Repository Resource:

 WaterOpticalConstants

Source Notebook

Obtain optical constants of water valid from ultraviolet to microwave range

Contributed by: Julián Laverde

ResourceFunction["WaterOpticalConstants"][]

returns the optical constants of water at T=23°C and P=1bar for the wavelength of 600 nm.

ResourceFunction["WaterOpticalConstants"][assoc]

returns the optical constants of water for the conditions specified in the Association assoc.

Details and Options

In ResourceFunction["WaterOpticalConstants"][assoc], the Association assoc can include the following elements:
"Wavelength"600 nmincident light wavelength
"Temperature23°Ctemperature of the water
"Pressure"1 barpressure of the water
ResourceFunction["WaterOpticalConstants"] returns the optical constants of water in liquid or ice (Ih) phase, corresponding to the selected temperature and pressure at the given wavelength.
The available optical constants are the refractive index and the absorption coefficient.
The refractive index is the ratio between the speed of light in medium to speed in a vacuum.
The absorption coefficient, also called the attenuation coefficient or extinction coefficient, is a representative term for determining how far the incident light of a certain wavelength penetrates a material before being absorbed. The corresponding unit is in reciprocal meters.
The wavelength can be any quantity whose physical dimension is "LengthUnit". If given only as a number, the default unit of wavelength is nanometers. If unspecified, wavelength is taken by default to be 600nm. The valid range ofwavelength is from 200nm to 1.0 x 109nm for the absorption coefficient and 10nm to 1.0 x1010nm for the refractive index.
The temperature can be any quantity whose physical dimension is "TemperatureUnit". If given only as a number, the default unit of temperature is degrees Celsius. If unspecified, temperature is taken by default to be 23°C. The maximum value of temperature is 500°C.
The value of pressure can be any quantity whose physical dimension is "PressureUnit". If given only as a number, the default unit of pressure is bars. If unspecified, pressure is taken by default to be 1 bar.
The valid range of temperature and pressure corresponds to conditions in which water exists in liquid or solid (Ih) phase.

Examples

Basic Examples (3) 

Use the default values:

In[1]:=
ResourceFunction["WaterOpticalConstants"][]
Out[1]=

Find the optical constants for a specified wavelength:

In[2]:=
ResourceFunction[ "WaterOpticalConstants"][<| "Wavelength" -> Quantity[250, "Nanometers"]|>]
Out[2]=

Or temperature:

In[3]:=
ResourceFunction[ "WaterOpticalConstants"][<| "Temperature" -> Quantity[-20, "DegreesCelsius"]|>]
Out[3]=

Scope (2) 

If the units of the input are not specified, it is assumed to be in the default units:

In[4]:=
ResourceFunction["WaterOpticalConstants"][<|"Wavelength" -> 500|>]
Out[4]=

Find the optical constants given specified values:

In[5]:=
ResourceFunction[ "WaterOpticalConstants"][<| "Wavelength" -> Quantity[700, "Nanometers"], "Temperature" -> Quantity[30, "DegreesCelsius"], "Pressure" -> Quantity[1, "Bars"]|>]
Out[5]=

Properties and Relations (1) 

Use Quantity to specify the units of the inputs:

In[6]:=
ResourceFunction[ "WaterOpticalConstants"][<| "Wavelength" -> Quantity[1, "Micrometers"]|>]
Out[6]=

Possible Issues (1) 

When the given wavelength is out of range for one of the optical constants, the value will be Missing:

In[7]:=
ResourceFunction[ "WaterOpticalConstants"][<| "Wavelength" -> Quantity[10, "Nanometers"]|>]
Out[7]=

Neat Examples (2) 

The function can be supplied to any suitable visualization function:

In[8]:=
Labeled[LogPlot[ ResourceFunction["WaterOpticalConstants"][<|"Wavelength" -> x|>][ "AbsorptionCoefficient"], {x, 200, 1000}], {"wavelength (nm)", "absorption coefficient (\!\(\*SuperscriptBox[\(m\), \(-1\)]\))"}, {Bottom, Left}, RotateLabel -> True]
Out[8]=

Find the color of the wavelength with the minimum absorption coefficient in the visible spectrum:

In[9]:=
wacList = Table[{ResourceFunction[ "WaterOpticalConstants"][<|"Wavelength" -> x|>][ "AbsorptionCoefficient"], x}, {x, 380, 750, 1}][[All, 1]]; Position[wacList, Min[wacList]] + 380; ColorData["VisibleSpectrum"][First@Flatten[%]]
Out[10]=

Publisher

WolframSpecialProjects

Version History

  • 1.0.0 – 21 December 2020

Source Metadata

  • Citation:
    • Pope, R. M., Fry, E. S., "Absorption spectrum (380–700 nm) of pure water. II. Integrating cavity measurements." Appl. Opt. vol. 36, 8710-8723, 1997. DOI: 10.1364/AO.36.008710
    • Quickenden, T. I., Irvin, J. A., "The ultraviolet absorption spectrum of liquid water." J. Chem Phys., vol. 72, 4416–4428, 1980. DOI: 10.1063/1.439733
    • Segelstein, D. J., "The complex refractive index of water." Thesis for: Master of Science, University of Missouri–Kansas City, 1981. https://mospace.umsystem.edu/xmlui/handle/10355/11599
    • Langford, V. S., McKinley, A. J., Quickenden, T. I., "Temperature Dependence of the Visible-Near-Infrared Absorption Spectrum of Liquid Water." J. Phys. Chem. A, vol. 105, no. 39, 8916–8921, 2001. DOI: 10.1021/jp010093m

License Information