ó ”¼™\c@ sÄdZddlmZmZdgZddlmZmZmZm Z m Z m Z m Z m Z mZmZddlmZddlmZmZmZejeeƒZdefd„ƒYZdS( sb This module has all the classes and functions related to waves in optics. **Contains** * TWave i’’’’(tprint_functiontdivisiontTWave( tsympifytpitsintcostsqrttSymboltStsymbolst Derivativetatan2(tExpr(tspeed_of_lighttmetertsecondcB sąeZdZdejdedƒd„Zed„ƒZ ed„ƒZ ed„ƒZ ed„ƒZ ed„ƒZ ed„ƒZed „ƒZed „ƒZd „ZeZd „Zd „Zd„Zd„Zd„ZRS(s  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. Arguments ========= amplitude : Sympifyable Amplitude of the wave. frequency : Sympifyable Frequency of the wave. phase : Sympifyable Phase angle of the wave. time_period : Sympifyable Time period of the wave. n : Sympifyable Refractive index of the medium. Raises ======= ValueError : When neither frequency nor time period is provided or they are not consistent. TypeError : When anything other than TWave objects is added. Examples ======== >>> from sympy import symbols >>> from sympy.physics.optics import TWave >>> A1, phi1, A2, phi2, f = symbols('A1, phi1, A2, phi2, f') >>> w1 = TWave(A1, f, phi1) >>> w2 = TWave(A2, f, phi2) >>> w3 = w1 + w2 # Superposition of two waves >>> w3 TWave(sqrt(A1**2 + 2*A1*A2*cos(phi1 - phi2) + A2**2), f, atan2(A1*cos(phi1) + A2*cos(phi2), A1*sin(phi1) + A2*sin(phi2))) >>> w3.amplitude sqrt(A1**2 + 2*A1*A2*cos(phi1 - phi2) + A2**2) >>> w3.phase atan2(A1*cos(phi1) + A2*cos(phi2), A1*sin(phi1) + A2*sin(phi2)) >>> w3.speed 299792458*meter/(second*n) >>> w3.angular_velocity 2*pi*f tncC st|ƒ}t|ƒ}t|ƒ}t|ƒ}t|ƒ}||_||_||_||_||_|dk rˆd|j|_n|dk rÕd|j|_|dk rÕ|d|krŅtdƒ‚qŅqÕn|dkrü|dkrütdƒ‚ndS(Nis/frequency and time_period should be consistent.s*Either frequency or time period is needed.(Rt _frequencyt _amplitudet_phaset _time_periodt_ntNonet ValueError(tselft amplitudet frequencytphaset time_periodR((s9lib/python2.7/site-packages/sympy/physics/optics/waves.pyt__init__Qs&             cC s|jS(s? Returns the frequency of the wave, in cycles per second. Examples ======== >>> from sympy import symbols >>> from sympy.physics.optics import TWave >>> A, phi, f = symbols('A, phi, f') >>> w = TWave(A, f, phi) >>> w.frequency f (R(R((s9lib/python2.7/site-packages/sympy/physics/optics/waves.pyRlscC s|jS(sI Returns the temporal period of the wave, in seconds per cycle. Examples ======== >>> from sympy import symbols >>> from sympy.physics.optics import TWave >>> A, phi, f = symbols('A, phi, f') >>> w = TWave(A, f, phi) >>> w.time_period 1/f (R(R((s9lib/python2.7/site-packages/sympy/physics/optics/waves.pyR~scC st|j|jS(sš Returns the wavelength (spatial period) of the wave, in meters per cycle. It depends on the medium of the wave. Examples ======== >>> from sympy import symbols >>> from sympy.physics.optics import TWave >>> A, phi, f = symbols('A, phi, f') >>> w = TWave(A, f, phi) >>> w.wavelength 299792458*meter/(second*f*n) (tcRR(R((s9lib/python2.7/site-packages/sympy/physics/optics/waves.pyt wavelengthscC s|jS(s! Returns the amplitude of the wave. Examples ======== >>> from sympy import symbols >>> from sympy.physics.optics import TWave >>> A, phi, f = symbols('A, phi, f') >>> w = TWave(A, f, phi) >>> w.amplitude A (R(R((s9lib/python2.7/site-packages/sympy/physics/optics/waves.pyR£scC s|jS(s5 Returns the phase angle of the wave, in radians. Examples ======== >>> from sympy import symbols >>> from sympy.physics.optics import TWave >>> A, phi, f = symbols('A, phi, f') >>> w = TWave(A, f, phi) >>> w.phase phi (R(R((s9lib/python2.7/site-packages/sympy/physics/optics/waves.pyR“scC s|j|jS(s Returns the propagation speed of the wave, in meters per second. It is dependent on the propagation medium. Examples ======== >>> from sympy import symbols >>> from sympy.physics.optics import TWave >>> A, phi, f = symbols('A, phi, f') >>> w = TWave(A, f, phi) >>> w.speed 299792458*meter/(second*n) (R R(R((s9lib/python2.7/site-packages/sympy/physics/optics/waves.pytspeedĘscC sdt|jS(sS Returns the angular velocity of the wave, in radians per second. Examples ======== >>> from sympy import symbols >>> from sympy.physics.optics import TWave >>> A, phi, f = symbols('A, phi, f') >>> w = TWave(A, f, phi) >>> w.angular_velocity 2*pi*f i(RR(R((s9lib/python2.7/site-packages/sympy/physics/optics/waves.pytangular_velocityŁscC sdt|jS(s_ Returns the wavenumber of the wave, in radians per meter. Examples ======== >>> from sympy import symbols >>> from sympy.physics.optics import TWave >>> A, phi, f = symbols('A, phi, f') >>> w = TWave(A, f, phi) >>> w.wavenumber pi*second*f*n/(149896229*meter) i(RR (R((s9lib/python2.7/site-packages/sympy/physics/optics/waves.pyt wavenumberėscC s*ddlm}t|ƒj||jƒS(s!String representation of a TWave.i’’’’(tsstr(tsympy.printingR$ttypet__name__targs(RR$((s9lib/python2.7/site-packages/sympy/physics/optics/waves.pyt__str__żsc C st|tƒrä|j|jkrÕ|j|jkrÕtt|jd|jdd|j|jt|j|j ƒƒ|j t |jt|jƒ|jt|jƒ|jt |jƒ|jt |jƒƒƒSt dƒ‚ntt|ƒjdƒ‚dS(s Addition of two waves will result in their superposition. The type of interference will depend on their phase angles. isJInterference of waves with different frequencies has not been implemented.s" and TWave objects can't be added.N(t isinstanceRRR RRRRRRRR RtNotImplementedErrort TypeErrorR&R'(Rtother((s9lib/python2.7/site-packages/sympy/physics/optics/waves.pyt__add__s$cO sD|jt|jtdƒ|jtdƒ|jtddtƒS(Ntxttitevaluate(RRR#RR"RRtFalse(RR(tkwargs((s9lib/python2.7/site-packages/sympy/physics/optics/waves.pyt_eval_rewrite_as_sins cO s6|jt|jtdƒ|jtdƒ|jƒS(NR/R0(RRR#RR"R(RR(R3((s9lib/python2.7/site-packages/sympy/physics/optics/waves.pyt_eval_rewrite_as_coss c O snddlm}tdƒ\}}}}|dƒ}t|||ƒ|dƒ||t|||ƒ|dƒS(Ni’’’’(tFunctionsmu, epsilon, x, ttEi(tsympyR6R R ( RR(R3R6tmutepsilonR/R0R7((s9lib/python2.7/site-packages/sympy/physics/optics/waves.pyt_eval_rewrite_as_pde"s cO sPddlm}m}|j|||jtdƒ|jtdƒ|jƒS(Ni’’’’(texptIR/R0(R8R<R=RR#RR"R(RR(R3R<R=((s9lib/python2.7/site-packages/sympy/physics/optics/waves.pyt_eval_rewrite_as_exp(s N(R't __module__t__doc__RR tZeroRRtpropertyRRR RRR!R"R#R)t__repr__R.R4R5R;R>(((s9lib/python2.7/site-packages/sympy/physics/optics/waves.pyRs(9     N(R@t __future__RRt__all__R8RRRRRRR R R R tsympy.core.exprR tsympy.physics.unitsRRRt convert_toRR(((s9lib/python2.7/site-packages/sympy/physics/optics/waves.pyts F