254 lines
7.0 KiB
Python
254 lines
7.0 KiB
Python
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"""
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**Contains**
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* Medium
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"""
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from sympy.physics.units import second, meter, kilogram, ampere
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__all__ = ['Medium']
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from sympy.core.basic import Basic
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from sympy.core.symbol import Str
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from sympy.core.sympify import _sympify
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from sympy.functions.elementary.miscellaneous import sqrt
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from sympy.physics.units import speed_of_light, u0, e0
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c = speed_of_light.convert_to(meter/second)
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_e0mksa = e0.convert_to(ampere**2*second**4/(kilogram*meter**3))
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_u0mksa = u0.convert_to(meter*kilogram/(ampere**2*second**2))
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class Medium(Basic):
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"""
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This class represents an optical medium. The prime reason to implement this is
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to facilitate refraction, Fermat's principle, etc.
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Explanation
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===========
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An optical medium is a material through which electromagnetic waves propagate.
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The permittivity and permeability of the medium define how electromagnetic
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waves propagate in it.
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Parameters
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==========
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name: string
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The display name of the Medium.
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permittivity: Sympifyable
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Electric permittivity of the space.
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permeability: Sympifyable
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Magnetic permeability of the space.
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n: Sympifyable
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Index of refraction of the medium.
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Examples
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========
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>>> from sympy.abc import epsilon, mu
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>>> from sympy.physics.optics import Medium
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>>> m1 = Medium('m1')
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>>> m2 = Medium('m2', epsilon, mu)
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>>> m1.intrinsic_impedance
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149896229*pi*kilogram*meter**2/(1250000*ampere**2*second**3)
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>>> m2.refractive_index
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299792458*meter*sqrt(epsilon*mu)/second
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References
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==========
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.. [1] https://en.wikipedia.org/wiki/Optical_medium
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"""
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def __new__(cls, name, permittivity=None, permeability=None, n=None):
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if not isinstance(name, Str):
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name = Str(name)
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permittivity = _sympify(permittivity) if permittivity is not None else permittivity
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permeability = _sympify(permeability) if permeability is not None else permeability
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n = _sympify(n) if n is not None else n
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if n is not None:
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if permittivity is not None and permeability is None:
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permeability = n**2/(c**2*permittivity)
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return MediumPP(name, permittivity, permeability)
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elif permeability is not None and permittivity is None:
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permittivity = n**2/(c**2*permeability)
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return MediumPP(name, permittivity, permeability)
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elif permittivity is not None and permittivity is not None:
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raise ValueError("Specifying all of permittivity, permeability, and n is not allowed")
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else:
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return MediumN(name, n)
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elif permittivity is not None and permeability is not None:
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return MediumPP(name, permittivity, permeability)
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elif permittivity is None and permeability is None:
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return MediumPP(name, _e0mksa, _u0mksa)
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else:
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raise ValueError("Arguments are underspecified. Either specify n or any two of permittivity, "
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"permeability, and n")
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@property
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def name(self):
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return self.args[0]
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@property
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def speed(self):
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"""
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Returns speed of the electromagnetic wave travelling in the medium.
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Examples
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========
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>>> from sympy.physics.optics import Medium
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>>> m = Medium('m')
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>>> m.speed
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299792458*meter/second
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>>> m2 = Medium('m2', n=1)
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>>> m.speed == m2.speed
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True
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"""
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return c / self.n
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@property
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def refractive_index(self):
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"""
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Returns refractive index of the medium.
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Examples
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========
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>>> from sympy.physics.optics import Medium
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>>> m = Medium('m')
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>>> m.refractive_index
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1
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"""
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return (c/self.speed)
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class MediumN(Medium):
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"""
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Represents an optical medium for which only the refractive index is known.
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Useful for simple ray optics.
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This class should never be instantiated directly.
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Instead it should be instantiated indirectly by instantiating Medium with
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only n specified.
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Examples
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========
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>>> from sympy.physics.optics import Medium
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>>> m = Medium('m', n=2)
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>>> m
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MediumN(Str('m'), 2)
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"""
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def __new__(cls, name, n):
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obj = super(Medium, cls).__new__(cls, name, n)
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return obj
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@property
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def n(self):
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return self.args[1]
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class MediumPP(Medium):
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"""
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Represents an optical medium for which the permittivity and permeability are known.
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This class should never be instantiated directly. Instead it should be
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instantiated indirectly by instantiating Medium with any two of
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permittivity, permeability, and n specified, or by not specifying any
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of permittivity, permeability, or n, in which case default values for
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permittivity and permeability will be used.
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Examples
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========
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>>> from sympy.physics.optics import Medium
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>>> from sympy.abc import epsilon, mu
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>>> m1 = Medium('m1', permittivity=epsilon, permeability=mu)
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>>> m1
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MediumPP(Str('m1'), epsilon, mu)
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>>> m2 = Medium('m2')
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>>> m2
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MediumPP(Str('m2'), 625000*ampere**2*second**4/(22468879468420441*pi*kilogram*meter**3), pi*kilogram*meter/(2500000*ampere**2*second**2))
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"""
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def __new__(cls, name, permittivity, permeability):
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obj = super(Medium, cls).__new__(cls, name, permittivity, permeability)
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return obj
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@property
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def intrinsic_impedance(self):
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"""
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Returns intrinsic impedance of the medium.
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Explanation
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===========
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The intrinsic impedance of a medium is the ratio of the
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transverse components of the electric and magnetic fields
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of the electromagnetic wave travelling in the medium.
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In a region with no electrical conductivity it simplifies
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to the square root of ratio of magnetic permeability to
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electric permittivity.
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Examples
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========
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>>> from sympy.physics.optics import Medium
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>>> m = Medium('m')
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>>> m.intrinsic_impedance
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149896229*pi*kilogram*meter**2/(1250000*ampere**2*second**3)
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"""
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return sqrt(self.permeability / self.permittivity)
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@property
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def permittivity(self):
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"""
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Returns electric permittivity of the medium.
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Examples
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========
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>>> from sympy.physics.optics import Medium
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>>> m = Medium('m')
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>>> m.permittivity
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625000*ampere**2*second**4/(22468879468420441*pi*kilogram*meter**3)
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"""
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return self.args[1]
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@property
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def permeability(self):
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"""
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Returns magnetic permeability of the medium.
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Examples
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========
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>>> from sympy.physics.optics import Medium
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>>> m = Medium('m')
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>>> m.permeability
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pi*kilogram*meter/(2500000*ampere**2*second**2)
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"""
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return self.args[2]
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@property
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def n(self):
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return c*sqrt(self.permittivity*self.permeability)
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