switching to high quality piper tts and added label translations

2026-01-29 23:48:19 +01:00
commit d80c619df9
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+"""
+**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)