Spaces:
Sleeping
Sleeping
File size: 7,124 Bytes
6a86ad5 |
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 |
"""
**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)
|