def test_lens_makers_formula():
n1, n2 = symbols('n1, n2')
m1 = Medium('m1', permittivity=e0, n=1)
m2 = Medium('m2', permittivity=e0, n=1.33)
assert lens_makers_formula(n1, n2, 10, -10) == 5 * n2 / (n1 - n2)
assert round(lens_makers_formula(m1, m2, 10, -10), 2) == -20.15
assert round(lens_makers_formula(1.33, 1, 10, -10), 2) == 15.15
def test_refraction_angle():
n1, n2 = symbols('n1, n2')
m1 = Medium('m1')
m2 = Medium('m2')
r1 = Ray3D(Point3D(-1, -1, 1), Point3D(0, 0, 0))
i = Matrix([1, 1, 1])
n = Matrix([0, 0, 1])
normal_ray = Ray3D(Point3D(0, 0, 0), Point3D(0, 0, 1))
P = Plane(Point3D(0, 0, 0), normal_vector=[0, 0, 1])
assert refraction_angle(r1, 1, 1, n) == Matrix([[1], [1], [-1]])
assert refraction_angle([1, 1, 1], 1, 1, n) == Matrix([[1], [1], [-1]])
assert refraction_angle((1, 1, 1), 1, 1, n) == Matrix([[1], [1], [-1]])
assert refraction_angle(i, 1, 1, [0, 0, 1]) == Matrix([[1], [1], [-1]])
assert refraction_angle(i, 1, 1, (0, 0, 1)) == Matrix([[1], [1], [-1]])
assert refraction_angle(i, 1, 1, normal_ray) == Matrix([[1], [1], [-1]])
assert refraction_angle(i, 1, 1, plane=P) == Matrix([[1], [1], [-1]])
assert refraction_angle(r1, 1, 1, plane=P) == \
Ray3D(Point3D(0, 0, 0), Point3D(1, 1, -1))
assert refraction_angle(r1, m1, 1.33, plane=P) == \
Ray3D(Point3D(0, 0, 0), Point3D(100/133, 100/133, -789378201649271*sqrt(3)/1000000000000000))
assert refraction_angle(r1, 1, m2, plane=P) == \
Ray3D(Point3D(0, 0, 0), Point3D(1, 1, -1))
assert refraction_angle(r1, n1, n2, plane=P) == \
Ray3D(Point3D(0, 0, 0), Point3D(n1/n2, n1/n2, -sqrt(3)*sqrt(-2*n1**2/(3*n2**2) + 1)))
assert refraction_angle(r1, 1.33, 1, plane=P) == 0 # TIR
assert refraction_angle(r1, 1, 1, normal_ray) == \
Ray3D(Point3D(0, 0, 0), direction_ratio=[1, 1, -1])
def test_refraction_angle():
n1, n2 = symbols('n1, n2')
m1 = Medium('m1')
m2 = Medium('m2')
r1 = Ray3D(Point3D(-1, -1, 1), Point3D(0, 0, 0))
i = Matrix([1, 1, 1])
n = Matrix([0, 0, 1])
normal_ray = Ray3D(Point3D(0, 0, 0), Point3D(0, 0, 1))
P = Plane(Point3D(0, 0, 0), normal_vector=[0, 0, 1])
assert refraction_angle(r1, 1, 1, n) == Matrix([[1], [1], [-1]])
assert refraction_angle([1, 1, 1], 1, 1, n) == Matrix([[1], [1], [-1]])
assert refraction_angle((1, 1, 1), 1, 1, n) == Matrix([[1], [1], [-1]])
assert refraction_angle(i, 1, 1, [0, 0, 1]) == Matrix([[1], [1], [-1]])
assert refraction_angle(i, 1, 1, (0, 0, 1)) == Matrix([[1], [1], [-1]])
assert refraction_angle(i, 1, 1, normal_ray) == Matrix([[1], [1], [-1]])
assert refraction_angle(i, 1, 1, plane=P) == Matrix([[1], [1], [-1]])
assert refraction_angle(r1, 1, 1, plane=P) == \
Ray3D(Point3D(0, 0, 0), Point3D(1, 1, -1))
assert refraction_angle(r1, m1, 1.33, plane=P) == \
Ray3D(Point3D(0, 0, 0), Point3D(Rational(100, 133), Rational(100, 133), -789378201649271*sqrt(3)/1000000000000000))
assert refraction_angle(r1, 1, m2, plane=P) == \
Ray3D(Point3D(0, 0, 0), Point3D(1, 1, -1))
assert refraction_angle(r1, n1, n2, plane=P) == \
Ray3D(Point3D(0, 0, 0), Point3D(n1/n2, n1/n2, -sqrt(3)*sqrt(-2*n1**2/(3*n2**2) + 1)))
assert refraction_angle(r1, 1.33, 1, plane=P) == 0 # TIR
assert refraction_angle(r1, 1, 1, normal_ray) == \
Ray3D(Point3D(0, 0, 0), direction_ratio=[1, 1, -1])
assert ae(refraction_angle(0.5, 1, 2), 0.24207, 5)
assert ae(refraction_angle(0.5, 2, 1), 1.28293, 5)
raises(ValueError, lambda: refraction_angle(r1, m1, m2, normal_ray, P))
raises(TypeError, lambda: refraction_angle(m1, m1, m2)
) # can add other values for arg[0]
raises(TypeError, lambda: refraction_angle(r1, m1, m2, None, i))
raises(TypeError, lambda: refraction_angle(r1, m1, m2, m2))
def test_brewster_angle():
m1 = Medium('m1', n=1)
m2 = Medium('m2', n=1.33)
assert round(brewster_angle(m1, m2), 2) == 0.93
m1 = Medium('m1', permittivity=e0, n=1)
m2 = Medium('m2', permittivity=e0, n=1.33)
assert round(brewster_angle(m1, m2), 2) == 0.93
def test_fresnel_coefficients():
assert all(
ae(i, j, 5)
for i, j in zip(
fresnel_coefficients(0.5, 1, 1.33), [0.11163, -0.17138, 0.83581, 0.82862]
)
)
assert all(
ae(i, j, 5)
for i, j in zip(
fresnel_coefficients(0.5, 1.33, 1), [-0.07726, 0.20482, 1.22724, 1.20482]
)
)
m1 = Medium("m1")
m2 = Medium("m2", n=2)
assert all(
ae(i, j, 5)
for i, j in zip(
fresnel_coefficients(0.3, m1, m2), [0.31784, -0.34865, 0.65892, 0.65135]
)
)
ans = [[-0.23563, -0.97184], [0.81648, -0.57738]]
got = fresnel_coefficients(0.6, m2, m1)
for i, j in zip(got, ans):
for a, b in zip(i.as_real_imag(), j):
assert ae(a, b, 5)
def test_lens_makers_formula():
n1, n2 = symbols("n1, n2")
m1 = Medium("m1", permittivity=e0, n=1)
m2 = Medium("m2", permittivity=e0, n=1.33)
assert lens_makers_formula(n1, n2, 10, -10) == 5 * n2 / (n1 - n2)
assert ae(lens_makers_formula(m1, m2, 10, -10), -20.15, 2)
assert ae(lens_makers_formula(1.33, 1, 10, -10), 15.15, 2)
def test_brewster_angle():
m1 = Medium('m1', n=1)
m2 = Medium('m2', n=1.33)
assert ae(brewster_angle(m1, m2), 0.93, 2)
m1 = Medium('m1', permittivity=e0, n=1)
m2 = Medium('m2', permittivity=e0, n=1.33)
assert ae(brewster_angle(m1, m2), 0.93, 2)
assert ae(brewster_angle(1, 1.33), 0.93, 2)
def test_lens_makers_formula_thick_lens():
n1, n2 = symbols('n1, n2')
m1 = Medium('m1', permittivity=e0, n=1)
m2 = Medium('m2', permittivity=e0, n=1.33)
assert ae(lens_makers_formula(m1, m2, 10, -10, d=1), -19.82, 2)
assert lens_makers_formula(
n1, n2, 1, -1,
d=0.1) == n2 / ((2.0 - (0.1 * n1 - 0.1 * n2) / n1) * (n1 - n2))
def test_fresnel_coefficients():
assert list(round(i, 5) for i in fresnel_coefficients(0.5, 1, 1.33)) == \
[0.11163, -0.17138, 0.83581, 0.82862]
assert list(round(i, 5) for i in fresnel_coefficients(0.5, 1.33, 1)) == \
[-0.07726, 0.20482, 1.22724, 1.20482]
m1 = Medium('m1')
m2 = Medium('m2', n=2)
assert list(round(i, 5) for i in fresnel_coefficients(0.3, m1, m2)) == \
[0.31784, -0.34865, 0.65892, 0.65135]
assert list(list(round(j, 5) for j in i.as_real_imag()) for i in \
fresnel_coefficients(0.6, m2, m1)) == \
[[-0.23563, -0.97184], [0.81648, -0.57738]]
def test_deviation():
n1, n2 = symbols('n1, n2')
m1 = Medium('m1')
m2 = Medium('m2')
r1 = Ray3D(Point3D(-1, -1, 1), Point3D(0, 0, 0))
n = Matrix([0, 0, 1])
i = Matrix([-1, -1, -1])
normal_ray = Ray3D(Point3D(0, 0, 0), Point3D(0, 0, 1))
P = Plane(Point3D(0, 0, 0), normal_vector=[0, 0, 1])
assert deviation(r1, 1, 1, normal=n) == 0
assert deviation(r1, 1, 1, plane=P) == 0
assert deviation(r1, 1, 1.1, plane=P).evalf(3) + 0.119 < 1e-3
assert deviation(i, 1, 1.1, normal=normal_ray).evalf(3) + 0.119 < 1e-3
assert deviation(r1, 1.33, 1, plane=P) is None # TIR
assert deviation(r1, 1, 1, normal=[0, 0, 1]) == 0
assert deviation([-1, -1, -1], 1, 1, normal=[0, 0, 1]) == 0
def test_lens_makers_formula_plano_lens():
n1, n2 = symbols('n1, n2')
m1 = Medium('m1', permittivity=e0, n=1)
m2 = Medium('m2', permittivity=e0, n=1.33)
assert ae(lens_makers_formula(m1, m2, 10, oo), -40.30, 2)
assert lens_makers_formula(n1, n2, 10, oo) == 10.0 * n2 / (n1 - n2)
def test_critical_angle():
m1 = Medium('m1', n=1)
m2 = Medium('m2', n=1.33)
assert ae(critical_angle(m2, m1), 0.85, 2)
def test_critical_angle():
m1 = Medium('m1', n=1)
m2 = Medium('m2', n=1.33)
assert round(critical_angle(m2, m1), 2) == 0.85
def test_critical_angle():
m1 = Medium("m1", n=1)
m2 = Medium("m2", n=1.33)
assert ae(critical_angle(m2, m1), 0.85, 2)