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| 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) | |