from sympy import sqrt, simplify
from sympy.physics.optics import Medium
from sympy.abc import epsilon, mu
from sympy.physics.units import speed_of_light, u0, e0, m, kg, s, A
c = speed_of_light.convert_to(m/s)
e0 = e0.convert_to(A**2*s**4/(kg*m**3))
u0 = u0.convert_to(m*kg/(A**2*s**2))
def test_medium():
m1 = Medium('m1')
assert m1.intrinsic_impedance == sqrt(u0/e0)
assert m1.speed == 1/sqrt(e0*u0)
assert m1.refractive_index == c*sqrt(e0*u0)
assert m1.permittivity == e0
assert m1.permeability == u0
m2 = Medium('m2', epsilon, mu)
assert m2.intrinsic_impedance == sqrt(mu/epsilon)
assert m2.speed == 1/sqrt(epsilon*mu)
assert m2.refractive_index == c*sqrt(epsilon*mu)
assert m2.permittivity == epsilon
assert m2.permeability == mu
# Increasing electric permittivity and magnetic permeability
# by small amount from its value in vacuum.
m3 = Medium('m3', 9.0*10**(-12)*s**4*A**2/(m**3*kg), 1.45*10**(-6)*kg*m/(A**2*s**2))
assert m3.refractive_index > m1.refractive_index
assert m3 > m1
# Decreasing electric permittivity and magnetic permeability
# by small amount from its value in vacuum.
**Contains**
* TWave
"""
from __future__ import print_function, division
__all__ = ['TWave']
from sympy import (sympify, pi, sin, cos, sqrt, Symbol, S, symbols, Derivative,
atan2)
from sympy.core.expr import Expr
from sympy.physics.units import speed_of_light, meter, second
c = speed_of_light.convert_to(meter / second)
class TWave(Expr):
r"""
This is a simple transverse sine wave travelling in a one-dimensional space.
Basic properties are required at the time of creation of the object,
but they can be changed later with respective methods provided.
It is represented as :math:`A \times cos(k*x - \omega \times t + \phi )`,
where :math:`A` is the amplitude, :math:`\omega` is the angular velocity,
:math:`k` is the wavenumber (spatial frequency), :math:`x` is a spatial variable
to represent the position on the dimension on which the wave propagates,
and :math:`\phi` is the phase angle of the wave.
from sympy import (symbols, Symbol, pi, sqrt, cos, sin, Derivative, Function,
simplify, I, atan2)
from sympy.abc import epsilon, mu
from sympy.functions.elementary.exponential import exp
from sympy.physics.units import speed_of_light, m, s
from sympy.physics.optics import TWave
c = speed_of_light.convert_to(m / s)
def test_twave():
A1, phi1, A2, phi2, f = symbols('A1, phi1, A2, phi2, f')
n = Symbol('n') # Refractive index
t = Symbol('t') # Time
x = Symbol('x') # Spatial variable
k = Symbol('k') # Wavenumber
E = Function('E')
w1 = TWave(A1, f, phi1)
w2 = TWave(A2, f, phi2)
assert w1.amplitude == A1
assert w1.frequency == f
assert w1.phase == phi1
assert w1.wavelength == c / (f * n)
assert w1.time_period == 1 / f
w3 = w1 + w2
assert w3.amplitude == sqrt(A1**2 + 2 * A1 * A2 * cos(phi1 - phi2) + A2**2)
assert w3.frequency == f
assert w3.wavelength == c / (f * n)
assert w3.time_period == 1 / f
assert w3.angular_velocity == 2 * pi * f
assert w3.wavenumber == 2 * pi * f * n / c
**Contains**
* TWave
"""
from __future__ import print_function, division
__all__ = ['TWave']
from sympy import (sympify, pi, sin, cos, sqrt, Symbol, S,
symbols, Derivative, atan2)
from sympy.core.expr import Expr
from sympy.physics.units import speed_of_light, meter, second
c = speed_of_light.convert_to(meter/second)
class TWave(Expr):
r"""
This is a simple transverse sine wave travelling in a one-dimensional space.
Basic properties are required at the time of creation of the object,
but they can be changed later with respective methods provided.
It is represented as :math:`A \times cos(k*x - \omega \times t + \phi )`,
where :math:`A` is the amplitude, :math:`\omega` is the angular velocity,
:math:`k` is the wavenumber (spatial frequency), :math:`x` is a spatial variable
to represent the position on the dimension on which the wave propagates,
and :math:`\phi` is the phase angle of the wave.
