""" **Contains** * Medium """ from sympy.physics.units import second, meter, kilogram, ampere __all__ = ['Medium'] from sympy.core.basic import Basic from sympy.core.symbol import Str from sympy.core.sympify import _sympify from sympy.functions.elementary.miscellaneous import 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)) class Medium(Basic): """ This class represents an optical medium. The prime reason to implement this is to facilitate refraction, Fermat's principle, etc. Explanation =========== 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] https://en.wikipedia.org/wiki/Optical_medium """ def __new__(cls, name, permittivity=None, permeability=None, n=None): if not isinstance(name, Str): name = Str(name) permittivity = _sympify(permittivity) if permittivity is not None else permittivity permeability = _sympify(permeability) if permeability is not None else permeability n = _sympify(n) if n is not None else n if n is not None: if permittivity is not None and permeability is None: permeability = n**2/(c**2*permittivity) return MediumPP(name, permittivity, permeability) elif permeability is not None and permittivity is None: permittivity = n**2/(c**2*permeability) return MediumPP(name, permittivity, permeability) elif permittivity is not None and permittivity is not None: raise ValueError("Specifying all of permittivity, permeability, and n is not allowed") else: return MediumN(name, n) elif permittivity is not None and permeability is not None: return MediumPP(name, permittivity, permeability) elif permittivity is None and permeability is None: return MediumPP(name, _e0mksa, _u0mksa) else: raise ValueError("Arguments are underspecified. Either specify n or any two of permittivity, " "permeability, and n") @property def name(self): return self.args[0] @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 >>> m2 = Medium('m2', n=1) >>> m.speed == m2.speed True """ return c / self.n @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) class MediumN(Medium): """ Represents an optical medium for which only the refractive index is known. Useful for simple ray optics. This class should never be instantiated directly. Instead it should be instantiated indirectly by instantiating Medium with only n specified. Examples ======== >>> from sympy.physics.optics import Medium >>> m = Medium('m', n=2) >>> m MediumN(Str('m'), 2) """ def __new__(cls, name, n): obj = super(Medium, cls).__new__(cls, name, n) return obj @property def n(self): return self.args[1] class MediumPP(Medium): """ Represents an optical medium for which the permittivity and permeability are known. This class should never be instantiated directly. Instead it should be instantiated indirectly by instantiating Medium with any two of permittivity, permeability, and n specified, or by not specifying any of permittivity, permeability, or n, in which case default values for permittivity and permeability will be used. Examples ======== >>> from sympy.physics.optics import Medium >>> from sympy.abc import epsilon, mu >>> m1 = Medium('m1', permittivity=epsilon, permeability=mu) >>> m1 MediumPP(Str('m1'), epsilon, mu) >>> m2 = Medium('m2') >>> m2 MediumPP(Str('m2'), 625000*ampere**2*second**4/(22468879468420441*pi*kilogram*meter**3), pi*kilogram*meter/(2500000*ampere**2*second**2)) """ def __new__(cls, name, permittivity, permeability): obj = super(Medium, cls).__new__(cls, name, permittivity, permeability) return obj @property def intrinsic_impedance(self): """ Returns intrinsic impedance of the medium. Explanation =========== 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 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.args[1] @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.args[2] @property def n(self): return c*sqrt(self.permittivity*self.permeability)