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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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