B [=@sdZddlmZddddddd d gZdd lmZmZmZmZm Z m Z m Z m Z dd l mZdd lmZddlmZddlmZddlmZdddZdddZddZddZdddZdddZdd Zdd ZdS)z **Contains** * refraction_angle * deviation * brewster_angle * lens_makers_formula * mirror_formula * lens_formula * hyperfocal_distance * transverse_magnification )divisionrefraction_angle deviationbrewster_anglelens_makers_formulamirror_formula lens_formulahyperfocal_distancetransverse_magnification)SymbolsympifysqrtMatrixacosooLimitatan2) is_sequence)Ray3D) intersection)Plane)MediumNcCs d}|dk r|dk rtdt|tsXt|r8t|}q\t|trNt|j}q\tdn|}|dk rt|tsvtdt|trd}||d}t|j }n|t|tst|rt|}nXt|tr t|j}t|trt||}t |dkrtdn d}|d}ntd n|}d \} } t|t r6|j } nt |} t|t rR|j } nt |} | | } ttd d |D} ttd d |D} || }|| }|| }d| dd|d}|jrdS| || |t||}|| }|s|St||dSdS)a1 This function calculates transmitted vector after refraction at planar surface. `medium1` and `medium2` can be `Medium` or any sympifiable object. If `incident` is an object of `Ray3D`, `normal` also has to be an instance of `Ray3D` in order to get the output as a `Ray3D`. Please note that if plane of separation is not provided and normal is an instance of `Ray3D`, normal will be assumed to be intersecting incident ray at the plane of separation. This will not be the case when `normal` is a `Matrix` or any other sequence. If `incident` is an instance of `Ray3D` and `plane` has not been provided and `normal` is not `Ray3D`, output will be a `Matrix`. Parameters ========== incident : Matrix, Ray3D, or sequence Incident vector medium1 : sympy.physics.optics.medium.Medium or sympifiable Medium 1 or its refractive index medium2 : sympy.physics.optics.medium.Medium or sympifiable Medium 2 or its refractive index normal : Matrix, Ray3D, or sequence Normal vector plane : Plane Plane of separation of the two media. Examples ======== >>> from sympy.physics.optics import refraction_angle >>> from sympy.geometry import Point3D, Ray3D, Plane >>> from sympy.matrices import Matrix >>> from sympy import symbols >>> n = Matrix([0, 0, 1]) >>> P = Plane(Point3D(0, 0, 0), normal_vector=[0, 0, 1]) >>> r1 = Ray3D(Point3D(-1, -1, 1), Point3D(0, 0, 0)) >>> refraction_angle(r1, 1, 1, n) Matrix([ [ 1], [ 1], [-1]]) >>> refraction_angle(r1, 1, 1, plane=P) Ray3D(Point3D(0, 0, 0), Point3D(1, 1, -1)) With different index of refraction of the two media >>> n1, n2 = symbols('n1, n2') >>> refraction_angle(r1, n1, n2, n) Matrix([ [ n1/n2], [ n1/n2], [-sqrt(3)*sqrt(-2*n1**2/(3*n2**2) + 1)]]) >>> 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))) FNz%Either plane or normal is acceptable.z/incident should be a Matrix, Ray3D, or sequencez3plane should be an instance of geometry.plane.PlaneTrz.Normal isn't concurrent with the incident ray.z-Normal should be a Matrix, Ray3D, or sequence)NNcSsg|] }|dqS)).0irr9lib/python3.7/site-packages/sympy/physics/optics/utils.py sz$refraction_angle..cSsg|] }|dqS)rr)rrrrrrsrr)direction_ratio) ValueError isinstancerrrr TypeErrorrr normal_vectorlenrrefractive_indexr r sumdotZ is_negative)incidentmedium1medium2normalplaneZ return_ray _incidentZintersection_pt_normaln1n2Zeta mag_incident mag_normalZc1Zcs2Zdrsrrrr"sl;                  c CsFt|||||d}|dkrBt|tr0t|j}t|tslt|rLt|}qpt|trbt|j}qptdn|}|dkrt|tst|rt|}qt|trt|j}qtdq|}n t|j}tt dd|D}tt dd|D} tt d d|D} ||}|| }|| }t | |} t | |} | | SdS) a1 This function calculates the angle of deviation of a ray due to refraction at planar surface. Parameters ========== incident : Matrix, Ray3D, or sequence Incident vector medium1 : sympy.physics.optics.medium.Medium or sympifiable Medium 1 or its refractive index medium2 : sympy.physics.optics.medium.Medium or sympifiable Medium 2 or its refractive index normal : Matrix, Ray3D, or sequence Normal vector plane : Plane Plane of separation of the two media. Examples ======== >>> from sympy.physics.optics import deviation >>> from sympy.geometry import Point3D, Ray3D, Plane >>> from sympy.matrices import Matrix >>> from sympy import symbols >>> n1, n2 = symbols('n1, n2') >>> n = Matrix([0, 0, 1]) >>> P = Plane(Point3D(0, 0, 0), normal_vector=[0, 0, 1]) >>> r1 = Ray3D(Point3D(-1, -1, 1), Point3D(0, 0, 0)) >>> deviation(r1, 1, 1, n) 0 >>> deviation(r1, n1, n2, plane=P) -acos(-sqrt(-2*n1**2/(3*n2**2) + 1)) + acos(-sqrt(3)/3) )r+r,rz/incident should be a Matrix, Ray3D, or sequenceNz-normal should be a Matrix, Ray3D, or sequencecSsg|] }|dqS)rr)rrrrrrszdeviation..cSsg|] }|dqS)rr)rrrrrrscSsg|] }|dqS)rr)rrrrrrs) rr!rrrrr"r#r r&rr') r(r)r*r+r,Z refractedr-r.r1r2Z mag_refractedrrrrrrsF$            cCsFd\}}t|tr|j}nt|}t|tr4|j}nt|}t||S)a This function calculates the Brewster's angle of incidence to Medium 2 from Medium 1 in radians. Parameters ========== medium 1 : Medium or sympifiable Refractive index of Medium 1 medium 2 : Medium or sympifiable Refractive index of Medium 1 Examples ======== >>> from sympy.physics.optics import brewster_angle >>> brewster_angle(1, 1.33) 0.926093295503462 )NN)r!rr%r r)r)r*r/r0rrrrs  cCsdt|tr|j}nt|}t|tr,|j}nt|}t|}t|}d|||d|d|S)aD This function calculates focal length of a thin lens. It follows cartesian sign convention. Parameters ========== n_lens : Medium or sympifiable Index of refraction of lens. n_surr : Medium or sympifiable Index of reflection of surrounding. r1 : sympifiable Radius of curvature of first surface. r2 : sympifiable Radius of curvature of second surface. Examples ======== >>> from sympy.physics.optics import lens_makers_formula >>> lens_makers_formula(1.33, 1, 10, -10) 15.1515151515151 r)r!rr%r )Zn_lensZn_surrZr1Zr2rrrr#s  cCs0|r|r|rtdt|}t|}t|}|tkr>> from sympy.physics.optics import mirror_formula >>> from sympy.abc import f, u, v >>> mirror_formula(focal_length=f, u=u) f*u/(-f + u) >>> mirror_formula(focal_length=f, v=v) f*v/(-f + v) >>> mirror_formula(u=u, v=v) u*v/(u + v) z"Please provide only two parametersuvfN)r r rr rdoit) focal_lengthr4r5_u_v_frrrrKsF $ $   $  cCs0|r|r|rtdt|}t|}t|}|tkr>> from sympy.physics.optics import lens_formula >>> from sympy.abc import f, u, v >>> lens_formula(focal_length=f, u=u) f*u/(f + u) >>> lens_formula(focal_length=f, v=v) f*v/(f - v) >>> lens_formula(u=u, v=v) u*v/(u - v) z"Please provide only two parametersr4r5r6N)r r rr rr7)r8r4r5r9r:r;rrrrsF $ $   $  cCs,t|}t|}t|}d|||dS)a Parameters ========== f: sympifiable Focal length of a given lens N: sympifiable F-number of a given lens c: sympifiable Circle of Confusion (CoC) of a given image format Example ======= >>> from sympy.physics.optics import hyperfocal_distance >>> from sympy.abc import f, N, c >>> round(hyperfocal_distance(f = 0.5, N = 8, c = 0.0033), 2) 9.47 rr)r )r6Ncrrrr scCst|}t|}|| S)au Calculates the transverse magnification, which is the ratio of the image size to the object size. Parameters ========== so: sympifiable Lens-object distance si: sympifiable Lens-image distance Example ======= >>> from sympy.physics.optics import transverse_magnification >>> transverse_magnification(30, 15) -2 )r )ZsiZsorrrr s)NN)NN)NNN)NNN)__doc__Z __future__r__all__Zsympyr r r rrrrrZsympy.core.compatibilityrZsympy.geometry.linerZsympy.geometry.utilrZsympy.geometry.planerZmediumrrrrrrrr r rrrr s0 (       Q$( E D