"""
**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)