WPC' %A&T$Ӭ9 5λ@Ȟ% IO-Ծ=;%'cわ yE@zr:)7ڝcn% ?ݕ@oΤE~p2E0Ph2}ŝTTBоؑA`ˮ/ab[꘏;mxxw.EM @M\.@'As{ߦN,d1&GHL]y OlJ]4𩜾 >fv;V>&sRJo_~pdT&4K½ڒ\FRs#E*rBn魯T2*k|{NI'--01G+>FSȪtuZl 8t5RTOaa l?LWv0nBhwYr/G:%V?)ky?s͑ Q M jTaSE #laU>N %U>` ` 0O D+  0O 0C- AMp  d7  df(  d 1d7Idf'd)))=dW>DdWAdWDqdWY deBdhC&dW&(dWN:dEgdX!d%%GJdX!d% &/d6Ud5,d"dW&n6 04#N^ w4 m 0Pbhpds d</!k"d#_%d&UN'* `&CG Times 12ptWPX '  PHYSICS-414 Optics Pre-Quiz 2pre-quiz (Earl C. Swallow(0Earl C. Swallow .   * `&CG Times 14ptWP('2S$ GU!   'dxd Level 1 Level 2 Level 3 Level 4 Level 5('2S$ GU!   ($      A<< c {df}over{dx}{1?^dfKMdx {d^2f}over{dx^2} X*-XXPjd2XXjfXX@Cdx2 Int_0^1`f`(x)`dx XXDL;130XXfXXi(XXxXX)XXcdx {dg}over{dt} X*XX@NdgXXVCdt {d^2g}over{dt^2} X*-XX@jd2XXjgXXVCdt2 Int_0{vert50inf}`g(t)`dt XXDL30XX2XXagXX(XX tXXC)XXdt 3A{vert80horz50>}~+~B{vert80horz50>} XXCAXX-XX CXXCBXX 4A{vert80horz-50->}~~B{vert80horz-50->} XXCAXX-XX CXXCBXX 7A{vert80horz-50->}~cdot~B{vert80horz-50->} XXCAXX-XX CXXCBXX :A{vert80horz-50->}~TIMES~B{vert80horz-50->} XXCAXX-XX C'XXCBXX OLINE`A{vert80horz50>}`LINE~\and~LINE`B{vert80horz50>}`LINE XXC XXCAXXXX7C XXCandXXkC XXCBXXXXC  8A{vert80horz50>}~\and~B{vert80horz50>}`. XXCAXX-XX CandXXCBXXXXAC. {PARTIALF}over{PARTIALx} }X*XX@N,XXNFXXQC,XXCx {PARTIALF}over{PARTIALy} }X*XX@N,XXNFXXQC,XXCy 0{PARTIAL^{``2}`F}over{PARTIAL`x`PARTIAL`y} C X*XXvN,2XXWNFXX@C,XXCxXX.C,XXCy ;GRAD{vert80horz50>}~cdot~E{vert80horz50>} XXC+XX9XXCXXCEXX E{vert80horz50>} XXCEXX- =GRAD{vert80horz50>}~TIMES~E{vert80horz50>} XXC+XX9XXC'XXCEXX E{vert80horz50>} XXCEXX- GRAD{vert80horz50>}`V XXC+XX9XXCV GRAD^{``2}`V XXC+2XXCV "func{U~=~Ae^{i(kx``omega`t)}} XXCUXXCXXCAei!(MkxK3t) func{v~=~omegaoverk} XXvXXXXXN3XXCk#|n * `&CG Times 12ptWPXXw PS+GXP* `&CG Times 14ptWP PK+GP* `$CG Times 6ptWP,,< P+G,P* `&CG Times 10ptWPd P[+GP( U$  HP LaserJet 5P/5MP PostScript0- ,$aU((3$ GU!   - - ~A{vert80horz50>}~=~2ihat~~jhat~+~khat~\and~B{vert80horz50>}~=~ihat~+~3jhat~~2khat`. XXCAXX-XX CXXC2XXjqXXSCiXXCXXqXXCjXXcCXXhqXXACkXXCandXXuCBXXXXiCXX^ qXXG CiXX CXX C3XX? qXX( CjXX CXX C2XX0 qXX CkXXw C. ifunc{{PARTIAL^{``2}`U}over{PARTIAL`x^2}~=~{1}over{v^2}~{PARTIAL^{``2}`U}over{PARTIAL`t^2}} X$-XX:j,2XXjUXXPC,XXCxZ2XX"X -XXUj1XX#Cv2Xm-XXj, 2XXdjUXXC,XX1Ct2 G~=~left[matrix{1&2#3&4}right]~;~~~H~=~left[matrix{5&3#2&1}right]~;~~~V~=~left[matrix{2#6}right] XXGXXXXpvXX+xXXxXXwXXkp}XXk+XXkXXk~XX 1XX2XX C3XXC4XX;XX;HXX#XXpvXX+xXXxXXwXXp}XX+XXXX~XX15XX%3XX1C2XX%C1XX ;XX_ VXX1 XX pvXX +xXX xXX wXX p}XX +XX XX ~XX? 2XX? C6 UE{vert80horz50>}`(x,``y,``z)~=~x`y`{ihat}~+~x`z`{jhat}~+~y`z`{khat} XXCEXX-XXC(XXCxXXgC,XXCyXXC,XXCzXXC)XXkCXXICxXXCyXX<qXX%CiXXCXXCxXX CzXXqXXnCjXXCXXCyXXS CzXX qXX Ck(I Z6Times New Roman Regular GU!   _XXU8XXdd8`YlEarlC.Swallow@EE*PreQuizD(#ModernOptics  @.1.0  f(x)=5x2(32x) Z(#(#   a. ` Evaluate:G73z X S p @@@EL . W]W] f  . ~   b. ` Evaluate:G73z X  p @@@EL >>      c. ` Evaluate:G73z X  p @@@EL 66 #U ;  2.  g(t)=_Ae__bt_;b>0 5   a. ` Evaluate:G73z X ` p @@@EL 00 A  Y   b. ` Evaluate:G73z X  p @@@EL >> X$  p   c. ` Evaluate:G73z X  p @@@EL o RR  o  3.0  Whataretherealandimaginarypartsof_ei-_?% !(#(#   &" 4.  VWG73z X  p @@@E i i@R    a. ` Evaluate:G73z X  p @@@EL *QQ b, *z   b. ` Evaluate: G73z X  p @@@EL QQ ,     c. ` Evaluate:!"G73z X  p @@@EL NQNQ &  >    d. ` Evaluate:#$G73z X  p @@@EL PQQ   P    e. ` Evaluate:%&G73z X  p @@@EL QQ       f. ` Findthecosineoftheanglebetween'(G73z X  p @@@EQQHL  d  5.  F(_x,y_)=6x2y3+3y+92    a. ` Evaluate:)*G73z X l p @@@EL LL       b. ` Evaluate:+,G73z X l p @@@EL #LL # #%   c. ` Evaluate:-.G73z X q p @@@EL &."." $& &<"   *o% 6.0  ^_G73z X  p @@@E& & @ Y(#(#   a. ` Evaluate:12G73z X  p @@@EL ZQZQ ߀(thedivergenceof34G73z X  p @@@E*bZA).    b. ` Evaluate:56G73z X  p @@@EL QQ $ (߀(thecurlof78G73z X  p @@@El  ZA).  < 7.0  V(_x,y,z_)=x2+_xy_Ԁ+_xz_` (#(# 0  a. ` Evaluate:9:G73z X  p @@@EL ff A߀(thegradientofV). (#(#   b. ` Evaluate:;<G73z X  p @@@EL L 5߀(the_Laplacian_ԀofV). F  8.0  Z[G73z X - p @@@E*>*>@߀_is_Ԁasimplewaveequation.Showthat?@G73z X l p @@@E~,,)߀isa  solution ifandonlyif ABG73z X  p @@@E8p4.(#(# 9.  \]G73z X  p @@@E m m@ *   a. ` Evaluate:_GH_ X    b. ` Evaluate:HG |"   c. ` Evaluate:_GV_ $   d. ` Evaluate:_GT_(thetransposeofG) &"   e. ` Evaluate:det[G](thedeterminantofG) (8$