203 lines
8.4 KiB
Python
203 lines
8.4 KiB
Python
|
from sympy.core.numbers import comp, Rational
|
||
|
|
from sympy.physics.optics.utils import (refraction_angle, fresnel_coefficients,
|
||
|
|
deviation, brewster_angle, critical_angle, lens_makers_formula,
|
||
|
|
mirror_formula, lens_formula, hyperfocal_distance,
|
||
|
|
transverse_magnification)
|
||
|
|
from sympy.physics.optics.medium import Medium
|
||
|
|
from sympy.physics.units import e0
|
||
|
|
|
||
|
|
from sympy.core.numbers import oo
|
||
|
|
from sympy.core.symbol import symbols
|
||
|
|
from sympy.functions.elementary.miscellaneous import sqrt
|
||
|
|
from sympy.matrices.dense import Matrix
|
||
|
|
from sympy.geometry.point import Point3D
|
||
|
|
from sympy.geometry.line import Ray3D
|
||
|
|
from sympy.geometry.plane import Plane
|
||
|
|
|
||
|
|
from sympy.testing.pytest import raises
|
||
|
|
|
||
|
|
|
||
|
|
ae = lambda a, b, n: comp(a, b, 10**-n)
|
||
|
|
|
||
|
|
|
||
|
|
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_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_deviation():
|
||
|
|
n1, n2 = symbols('n1, n2')
|
||
|
|
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
|
||
|
|
assert ae(deviation(0.5, 1, 2), -0.25793, 5)
|
||
|
|
assert ae(deviation(0.5, 2, 1), 0.78293, 5)
|
||
|
|
|
||
|
|
|
||
|
|
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_critical_angle():
|
||
|
|
m1 = Medium('m1', n=1)
|
||
|
|
m2 = Medium('m2', n=1.33)
|
||
|
|
assert ae(critical_angle(m2, m1), 0.85, 2)
|
||
|
|
|
||
|
|
|
||
|
|
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) == 5.0*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_mirror_formula():
|
||
|
|
u, v, f = symbols('u, v, f')
|
||
|
|
assert mirror_formula(focal_length=f, u=u) == f*u/(-f + u)
|
||
|
|
assert mirror_formula(focal_length=f, v=v) == f*v/(-f + v)
|
||
|
|
assert mirror_formula(u=u, v=v) == u*v/(u + v)
|
||
|
|
assert mirror_formula(u=oo, v=v) == v
|
||
|
|
assert mirror_formula(u=oo, v=oo) is oo
|
||
|
|
assert mirror_formula(focal_length=oo, u=u) == -u
|
||
|
|
assert mirror_formula(u=u, v=oo) == u
|
||
|
|
assert mirror_formula(focal_length=oo, v=oo) is oo
|
||
|
|
assert mirror_formula(focal_length=f, v=oo) == f
|
||
|
|
assert mirror_formula(focal_length=oo, v=v) == -v
|
||
|
|
assert mirror_formula(focal_length=oo, u=oo) is oo
|
||
|
|
assert mirror_formula(focal_length=f, u=oo) == f
|
||
|
|
assert mirror_formula(focal_length=oo, u=u) == -u
|
||
|
|
raises(ValueError, lambda: mirror_formula(focal_length=f, u=u, v=v))
|
||
|
|
|
||
|
|
|
||
|
|
def test_lens_formula():
|
||
|
|
u, v, f = symbols('u, v, f')
|
||
|
|
assert lens_formula(focal_length=f, u=u) == f*u/(f + u)
|
||
|
|
assert lens_formula(focal_length=f, v=v) == f*v/(f - v)
|
||
|
|
assert lens_formula(u=u, v=v) == u*v/(u - v)
|
||
|
|
assert lens_formula(u=oo, v=v) == v
|
||
|
|
assert lens_formula(u=oo, v=oo) is oo
|
||
|
|
assert lens_formula(focal_length=oo, u=u) == u
|
||
|
|
assert lens_formula(u=u, v=oo) == -u
|
||
|
|
assert lens_formula(focal_length=oo, v=oo) is -oo
|
||
|
|
assert lens_formula(focal_length=oo, v=v) == v
|
||
|
|
assert lens_formula(focal_length=f, v=oo) == -f
|
||
|
|
assert lens_formula(focal_length=oo, u=oo) is oo
|
||
|
|
assert lens_formula(focal_length=oo, u=u) == u
|
||
|
|
assert lens_formula(focal_length=f, u=oo) == f
|
||
|
|
raises(ValueError, lambda: lens_formula(focal_length=f, u=u, v=v))
|
||
|
|
|
||
|
|
|
||
|
|
def test_hyperfocal_distance():
|
||
|
|
f, N, c = symbols('f, N, c')
|
||
|
|
assert hyperfocal_distance(f=f, N=N, c=c) == f**2/(N*c)
|
||
|
|
assert ae(hyperfocal_distance(f=0.5, N=8, c=0.0033), 9.47, 2)
|
||
|
|
|
||
|
|
|
||
|
|
def test_transverse_magnification():
|
||
|
|
si, so = symbols('si, so')
|
||
|
|
assert transverse_magnification(si, so) == -si/so
|
||
|
|
assert transverse_magnification(30, 15) == -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_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)
|