docs: def grey_transmittance(extinction_coefficient, molar_density, length, base=e):
      r'''Calculates the transmittance of a grey body, given the extinction
      coefficient of the material, its molar density, and the path length of the 
      radiation.
      
      .. math::
          \tau = base^{(-\epsilon \cdot l\cdot \rho_m )}
  
      Parameters
      ----------
      extinction_coefficient : float
          The extinction coefficient of the material the radiation is passing at
          the modeled frequency, [m^2/mol]
      molar_density : float
          The molar density of the material the radiation is passing through,
          [mol/m^3]
      length : float
          The length of the body the radiation is transmitted through, [m]
      base : float, optional
          The exponent used in calculations; `e` is more theoretically sound but
          10 is often used as a base by chemists, [-]
  
      Returns
      -------
      transmittance : float
          The fraction of spectral radiance which is transmitted through a grey 
          body (can be liquid, gas, or even solid ex. in the case of glasses) [-]
  
      Notes
      -----
      For extinction coefficients, see the HITRAN database. They are temperature
      and pressure dependent for each chemical and phase.
  
      Examples
      --------
      Overall transmission loss through 1 cm of precipitable water equivalent
      atmospheric water vapor at a frequency of 1.3 um [2]_:
      
      >>> grey_transmittance(3.8e-4, molar_density=55300, length=1e-2)
      0.8104707721191062
  
      References
      ----------
      .. [1] Modest, Michael F. Radiative Heat Transfer, Third Edition. 3rd
         edition. New York: Academic Press, 2013.
      .. [2] Eldridge, Ralph G. "Water Vapor Absorption of Visible and Near 
         Infrared Radiation." Applied Optics 6, no. 4 (April 1, 1967): 709-13.
         https://doi.org/10.1364/AO.6.000709.
      '''
      transmittance = molar_density*extinction_coefficient*length
      return base**(-transmittance)