{VERSION 3 0 "SUN SPARC SOLARIS" "3.0" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 0 0 0 0 }{CSTYLE "2D Math" -1 2 "Times New Roman" 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 }{CSTYLE "2D Output" 2 20 "" 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 }{PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Text Output" -1 2 1 {CSTYLE "" -1 -1 "Courier" 1 10 0 0 255 1 0 0 0 0 0 1 3 0 3 }1 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Heading 1" 0 3 1 {CSTYLE "" -1 -1 "" 1 18 0 0 0 0 0 1 0 0 0 0 0 0 0 }1 0 0 0 8 4 0 0 0 0 0 0 -1 0 } {PSTYLE "Heading 2" 3 4 1 {CSTYLE "" -1 -1 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 8 2 0 0 0 0 0 0 -1 0 }{PSTYLE "Warning" 2 7 1 {CSTYLE "" -1 -1 "" 0 1 0 0 255 1 0 0 0 0 0 0 1 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Maple Output" 0 11 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 3 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "M aple Plot" 0 13 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 } 3 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }} {SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "with(linalg):\nwith( plots):" }}{PARA 7 "" 1 "" {TEXT -1 32 "Warning, new definition for no rm" }}{PARA 7 "" 1 "" {TEXT -1 33 "Warning, new definition for trace" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 28 "Thin Lens Modeling Worksheet" }}{PARA 0 "" 0 "" {TEXT -1 162 "This worksheet allows one to see how a thin lens model works. \+ By specifying the two focal points and a point in the world, the corre sponding focus point is shown." }}{PARA 0 "" 0 "" {TEXT -1 22 " \+ " }}{PARA 0 "" 0 "" {TEXT -1 24 "Ross Beveridge 2/23/ 99" }}{SECT 0 {PARA 4 "" 0 "" {TEXT -1 22 "The Lens Specification" }} {PARA 0 "" 0 "" {TEXT -1 136 "The left focal point, right focal point, and point on the left are given below. The center of the lens is assu med to be the origin [0,0]" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 43 "Fl := [-5, 0];\nFr := [5, 0];\nP : = [-10,3];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#FlG7$!\"&\"\"!" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%#FrG7$\"\"&\"\"!" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#>%\"PG7$!#5\"\"$" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 286 "The other points of interest, Q, R and p, are defined by the two \+ focal points and P. To solve for them, build parameters lines fromPR a nd intersect this with x=0. This yields the point R. Next, parameteriz e the line from Q through Fl and intersect it with y=Ry. This yields t he point p." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "Q := [0, P[2 ]];" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 57 "PR := [P[1] + (Fl[1] - P[1]) *t, P[2] + (Fl[2] - P[2])*t]:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 43 "R \+ := [0, subs(\{t=solve(PR[1]=0,t)\},PR[2])];" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 57 "Qp := [Q[1] + (Fr[1] - Q[1])*t, Q[2] + (Fr[2] - Q[2]) *t]:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 49 "p := [subs(\{t=solve(Qp[2]= R[2],t)\},Qp[1]), R[2]];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"QG7$\" \"!\"\"$" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"RG7$\"\"!!\"$" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"pG7$\"#5!\"$" }}}}{SECT 0 {PARA 4 "" 0 "" {TEXT -1 27 "The plot of the light paths" }}{PARA 0 "" 0 "" {TEXT -1 35 "Now we can plot the different paths" }}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 28 "Ps := [-12,1]:\nPe := [-7,6]:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 882 "objs := \{\}:\nfor s from 0.0 to 1 .0 by 0.10 do\n P := [Ps[1] + (Pe[1] - Ps[1])*s, Ps[2] + (Pe[2] - P s[2])*s]:\n Q := [0, P[2]]:\n PR := [P[1] + (Fl[1] - P[1])*t, P[2 ] + (Fl[2] - P[2])*t]:\n R := [0, subs(\{t=solve(PR[1]=0,t)\},PR[2] )]:\n Qp := [Q[1] + (Fr[1] - Q[1])*t, Q[2] + (Fr[2] - Q[2])*t]:\n \+ p := [subs(\{t=solve(Qp[2]=R[2],t)\},Qp[1]), R[2]]:\n h := s * 0.8 ;\n objs := \{op(objs),CURVES([P,Q],THICKNESS(3),COLOR(HUE,h))\}:\n \+ objs := \{op(objs),CURVES([P,R],THICKNESS(3),COLOR(HUE,h))\}:\n ob js := \{op(objs),CURVES([Q,p],THICKNESS(3),COLOR(HUE,h))\}:\n objs : = \{op(objs),CURVES([R,p],THICKNESS(3),COLOR(HUE,h))\}:\n objs := \{ op(objs),CURVES([P,p],THICKNESS(3),COLOR(HUE,h))\}:\n objs := \{op(o bjs),POINTS(P,SYMBOL(CIRCLE))\}:\n objs := \{op(objs),POINTS(p,SYMBO L(CIRCLE))\}:\n objs := \{op(objs),POINTS(Q,SYMBOL(CIRCLE))\}:\n o bjs := \{op(objs),POINTS(R,SYMBOL(CIRCLE))\}:\nod:" }}}{PARA 0 "" 0 " " {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 73 "display(o bjs,axes=NORMAL,view=[-15..20,-16..8],font=[HELVETICA,BOLD,14]);" }} {PARA 13 "" 1 "" {INLPLOT "6bq-%'CURVESG6%7$7$$!$](!\"#$\"$]&F*7$\"\"! 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