Source code for sympy.physics.optics.medium

"""
**Contains**

* Medium
"""

from __future__ import division
from sympy.physics.units import second, meter, kilogram, ampere

__all__ = ['Medium']

from sympy import Symbol, sympify, sqrt
from sympy.physics.units import speed_of_light, u0, e0


c = speed_of_light.convert_to(meter/second)
_e0mksa = e0.convert_to(ampere**2*second**4/(kilogram*meter**3))
_u0mksa = u0.convert_to(meter*kilogram/(ampere**2*second**2))


[docs]class Medium(Symbol): """ This class represents an optical medium. The prime reason to implement this is to facilitate refraction, Fermat's priciple, etc. An optical medium is a material through which electromagnetic waves propagate. The permittivity and permeability of the medium define how electromagnetic waves propagate in it. Parameters ========== name: string The display name of the Medium. permittivity: Sympifyable Electric permittivity of the space. permeability: Sympifyable Magnetic permeability of the space. n: Sympifyable Index of refraction of the medium. Examples ======== >>> from sympy.abc import epsilon, mu >>> from sympy.physics.optics import Medium >>> m1 = Medium('m1') >>> m2 = Medium('m2', epsilon, mu) >>> m1.intrinsic_impedance 149896229*pi*kilogram*meter**2/(1250000*ampere**2*second**3) >>> m2.refractive_index 299792458*meter*sqrt(epsilon*mu)/second References ========== .. [1] http://en.wikipedia.org/wiki/Optical_medium """ def __new__(cls, name, permittivity=None, permeability=None, n=None): obj = super(Medium, cls).__new__(cls, name) obj._permittivity = sympify(permittivity) obj._permeability = sympify(permeability) obj._n = sympify(n) if n is not None: if permittivity != None and permeability == None: obj._permeability = n**2/(c**2*obj._permittivity) if permeability != None and permittivity == None: obj._permittivity = n**2/(c**2*obj._permeability) if permittivity != None and permittivity != None: if abs(n - c*sqrt(obj._permittivity*obj._permeability)) > 1e-6: raise ValueError("Values are not consistent.") elif permittivity is not None and permeability is not None: obj._n = c*sqrt(permittivity*permeability) elif permittivity is None and permeability is None: obj._permittivity = _e0mksa obj._permeability = _u0mksa return obj @property def intrinsic_impedance(self): """ Returns intrinsic impedance of the medium. The intrinsic impedance of a medium is the ratio of the transverse components of the electric and magnetic fields of the electromagnetic wave travelling in the medium. In a region with no electrical conductivity it simplifies to the square root of ratio of magnetic permeability to electric permittivity. Examples ======== >>> from sympy.physics.optics import Medium >>> m = Medium('m') >>> m.intrinsic_impedance 149896229*pi*kilogram*meter**2/(1250000*ampere**2*second**3) """ return sqrt(self._permeability/self._permittivity) @property def speed(self): """ Returns speed of the electromagnetic wave travelling in the medium. Examples ======== >>> from sympy.physics.optics import Medium >>> m = Medium('m') >>> m.speed 299792458*meter/second """ return 1/sqrt(self._permittivity*self._permeability) @property def refractive_index(self): """ Returns refractive index of the medium. Examples ======== >>> from sympy.physics.optics import Medium >>> m = Medium('m') >>> m.refractive_index 1 """ return (c/self.speed) @property def permittivity(self): """ Returns electric permittivity of the medium. Examples ======== >>> from sympy.physics.optics import Medium >>> m = Medium('m') >>> m.permittivity 625000*ampere**2*second**4/(22468879468420441*pi*kilogram*meter**3) """ return self._permittivity @property def permeability(self): """ Returns magnetic permeability of the medium. Examples ======== >>> from sympy.physics.optics import Medium >>> m = Medium('m') >>> m.permeability pi*kilogram*meter/(2500000*ampere**2*second**2) """ return self._permeability def __str__(self): from sympy.printing import sstr return type(self).__name__ + sstr(self.args) def __lt__(self, other): """ Compares based on refractive index of the medium. """ return self.refractive_index < other.refractive_index def __gt__(self, other): return not self.__lt__(other) def __eq__(self, other): return self.refractive_index == other.refractive_index def __ne__(self, other): return not self.__eq__(other)