' +JJJJ ?\>m0M='+l> /+l   d]@ŵLҦ]]LF L}BBL] X  ` 鷎귭෍ᷩ췩緈JJJJx Lȿ L8ᷭ緍췩 緍i 8 `巬 췌`x (`(8`I`B` ``>J>J>VU)?`8'x0|&HhHh VY)'&Y)xꪽ)' `Hh`V0^*^*>&` aI꽌ɪVɭ&Y&&Y& 꽌ɪ\8`&&꽌ɪɖ'*&%&,E'зЮ꽌ɪФ`+*xS&x'8*3Ixix&& 8  '  & x)*++`FG8`0($ p,&"ųųೳŪŪųųij  !"#$%&'()*+,-./0123456789:;<=>?   1 '" *"( (9"1 ( ,.(0# 2  /#0/#0 *?'#07#00/0/'#07#0:"4<*55/**5/*%5/)1/)1/)1/)'#0/#0*5/*75/**5/*:5//#0/#0'#07#0:::*::'#07#0"):$(%"%:$(%"%$$2%4%$$2%4%$(2()!)E(!8b $!H(+ "@H !D)"E` @ $ C ` DQ &J80^݌Hh ü ü݌ ռ ռ ռA ļD ļ? ļAEDE?HJ>h Լ ռ ռ ռ`HJ>݌h Hh݌`葠葠ȔЖȔЖȠHIHHHHhHH݌hHhHh݌H6 VDP (ED Z $0x8x D- ܸDD# H8`?E Vk *f???0xE Hh D#-EEE8` D ܸx D - ܸx8`-0ݩ?ʥD EEE`   LDcpq` [` ~  LӜu`".Q`pNФbptťܥm2<(-Py0\|e<6e<g< JJJJj귍hI  aUL@ kU8  L  Q^R(jQ0l^l\  wUuW ԧ H h@ [_ /QSIRb_L`LLLL`ª`LQLYLeLXLeLee ўQH\(h0L& Ꝥ$`( R \ZLl8 ўR HH\`\Z[YS6`LxQɿu3'RͲʎRʎ]]]ɍuL͟ɍ}RLRɍg^H8 ^hZLɍR LͲɊRR% QLܤͲ Z@ -^ ş\[Z QY\[Z8`l6Lş_Ȍb_Ͳ] )Y h( ֭ͲLɍ [LLĦ__ ^ 9 LҦ3 9 a   0LjLY u< (_9 ˭ɠuɠK_9 ?LˆʎõĵL õ ĵµ aµ`` L̦µ_bJLuLz`  ȟ QlXJ̥KlV  ȟ QlV eօ3L e3L &RL &QL d L4 Ne)n `@-eff L f`L . tQLѤ LҦL` OPu d L Ne)noon 8ɍ` ^f\õL ^NR  RΩLҦ)\Z ʽ LHv 3h`0h8` [L NС õ`A@` ŵL^Lõ`  \ 濭0 \  ȟ Q ^\lZl^?cqH şch`fhjõĵ@OAP`u@`@&`QR`E Ls  @DAE@u`8` %@ @A@`@`@A`Mµ ) LЦ`8@AWc@8@-@HAȑ@hHȑ@ȑ@hHȑ@Ȋ@ch8&ȑ@Hȑ@Ah@LHȑ@ȑ@ htphso`hMhL`9V8U897T6S67`INILOASAVRUCHAIDELETLOCUNLOCCLOSREAEXEWRITPOSITIOOPEAPPENRENAMCATALOMONOMOPRINMAXFILEFINBSAVBLOABRUVERIF!pppp p p p p`" t""#x"p0p@p@@@p@!y q q p@  LANGUAGE NOT AVAILABLRANGE ERROWRITE PROTECTEEND OF DATFILE NOT FOUNVOLUME MISMATCI/O ERRODISK FULFILE LOCKESYNTAX ERRONO BUFFERS AVAILABLFILE TYPE MISMATCPROGRAM TOO LARGNOT DIRECT COMMANč$3>L[dmx- (  @|Ϡ@跻~!Wo*9~~~~ɬƬ~_ j ʪHɪH`Lc (L ܫ㵮赎 ɱ^_ J QL_Ls贩紎 DǴҵԵƴѵӵµȴ 7 ַ :ŵƴѵǴҵȴµ納贍﵎ٵ്ᵭⳍڵL^ѵ-I `  4 ò-յ!  8صٵ紭ﵝ 7L (0+BC  7L HH`LgL{0 HH` õL H hBL BH [ h`Lo õ ڬL B ڬ LʬH hB@ յյ [L (ȴ) ȴ 7L L ( L (ȴL{ƴѵ洩ƴǴҵ 7 ^* B0 HȱBh ӵԵ 8 L8 ݲ` ܫ  / / ED B / / ]ƴS0Jȴ ȴ)  紅D贅E B ƴ  / 0L Ν `HD٤DEEhiHLGh ` ŵBѵ-` ѵB-` ܫ XI볩쳢8 DH E𳈈췍Ȍ X0 · JLǵBȵC`,յp` 䯩 R-յյ`յ0` K R-յյ`ɵʵӵԵ` 4 K ( ѵҵLBȱBL8` DBHBH : ַ޵BȭߵBhhӵԵ RBܵmڵ޵ȱBݵm۵ߵ` 䯩LR˵̵ֵ׵`êĪLR E( 8` R` ELRŪƪ`췌 յյI뷭鷭귭ⵍ㵍跬ª 뷰` Lf ݵܵߵ޵ ^`8ܵ i B8` 4L ֵȱB׵ ܯ䵍൭嵍 ` DȑB׵Bֵ  ַ յյ`굎뵎쵬 뵎쵌``õĵBCõĵ`µµ`L õBĵCصص Qƴ0"Bƴ 󮜳` 0۰ϬBƴ8`i#`ЗLw!0>ﵭ` m ﳐ 7i볍 8 ЉLw`H h ݲL~ `浍국䵍뵩嵠Jm赍嵊mjnnn浈ۭm浍浭m䵍䵩m嵍`"L ŵ8ŵH ~(` d ֠z# u`E."O:"YOU WILL GET TO MOVE AN OBJECT AROUND INFRONT OF A LENS OR MIRROR." :"THE COMPUTER WILL DRAW RAY DIAGRAMS AND SHOW WHAT TYPE OF IMAGE IS FORMED."$::"PRESS 1 TO USE A CONVEX LENS."%" 2 TO USE A CONCAVE LENS."E ARROW -::7:12:"OPTICS EXPERIMENT"a20:24:"COPYRIGHT 1981":24:"BY MARK CROSS"m15000~I12222:I63999:SET UP START OF SHAPE TABLE APPENDED TO THIS PROGRAM":2:"THIS EXPERIMENT SHOWS YOU HOW LIGHT RAYSFORM AN IMAG3ıXX8C7TH:X,YI:X:Q(X1C3)H1ı: GET IMAGE FOR CONCAVE MIRRORnXIXCJ1(XCX1)(C3X1)YIYB(YBY1)(XCXI)(XCX1)YJYIC8H1(YIYB)XIC8XIG7YIC8ıXI,YB1XI,YIXIC8,YJXIC8,YJXI,YI:: DRAW THE IMAG%XXCX3TH:X,YB(XXC)M0:X:Y CONCAVE MIRROR: IN PARALLEL, OUT THROUGHT F }X1W,Y1176,Y1C5,160:X1C3ıYY1THTH:176(Y1Y)M2,Y:Y: CONCAVE MIRROR RAY IN THROUGH F X8XCABqYB)TX1,Y1X8W,YIW,YI:X1C000 @>@>3:CO(4) @ @ @0@I:YU @p@@SE ONE.. @@ d5RATI""""""   (Y$):R$****100 6000 ONSTV@@@@@V:p@8@p@8 @@ 200,U```@@00,3200,@@ 000 "-$ " - $@T IN$@ON ""T @ 0SY  @@S10:@@0@IN @ DlS3266 THAT PA@@`J016: >" )  >")  @@T IT TAK 16:Z):Z  OST OFTE@@PnC5)* NXX1İ120:80:3200=* Z:208:90:148:150:165K* X1NX:TH}* COUNTCOUNTW(X1C3):COUNTH1COUNTZ:3110* 3140*CH8:CV17:M$"VIRTUAL REAL":10*CH8:M$"ERECT INVERTED":10+CH8:CVCV.5:M$"ENLARGED REDUCE5:300)& 80: DRAW AXIS2)0 120:CONCAVE LENSK)D 90: DRAW OBJECT ^)N 143: RAY 1p)S 150: RAY 2y)b 160)l 200) KEY(KB):SB,Z) NXX1:KEYG1KEYG2KEYH7NXX1DX(X1G4)) KEYG315000* KEYC9KEYG0KEYG9NXX1DX(X1CONTROL SECTION 9( X6207:Y6Z:X4101:Y479:G4130:DX4N( :3:1:0:X165[( 80:120( M$"< MOVE OBJECT LEFT":CH0:CV21:10( M$"> MOVE OBJECT RIGHT":10( M$"Q QUIT":10(! M$"CONCAVE LENS":CH15:CV0:10(" 4000)# XI120:YI5000.'< KEYC9KEYG0KEYG9NXX1DX(X1C5)I'F NXX1İ330:370:2600r'P Z:348:364:385:X1C8,Y1X1C8,Y1'Q X1,G8X1,Y1X1C8,Y1C8X1C8,Y1C8X1,Y1:80X1T,H8'Z X1NX:TH'd Z1Z1W:Z1H1Z1Z:2580'n 2590' CONCAVE LENS ( 5J1,136:65J1,144:65130,156=& 330:370: MIRROR + AXISF& 350Y& 343:380:360& X1,G8X1,Y1X1C8,Y1C8X1C8,Y1C8X1,Y1& 80X1T,H8&" X1,Y1X1H5,Y1&( KEY(KB):SB,Z&2 NXX1:KEYG1KEYG2KEYH7NXX1DX(X1H7)'7 KEYG315230:M21.533:A.005:DX4:J150:H91932% M3045>% :W:ZF% THs% M$"< MOVE OBJECT LEFT":CH0:CV21:10% M$"> MOVE OBJECT RIGHT":10% M$"Q QUIT":10% M$"CONVEX MIRROR":CV0:CH20:10% 4000% X180:Y150:XI200:YI40& 6NXX1İ410:2110.$W0:65212,16813(X1C3)V$\Z:451:430:425:(YIYB)J1İ445$aX1,G8X1,Y1X1C8,Y1C8X1C8,Y1C8X1,Y1$b80X1T,Y1H1$fX1NX:TH$pZ1Z1W:Z1H1Z1Z:2080$z2090$ CONVEX MIRROR &% XC180:G6110:F3204:F4,Y1X1C8,Y1C8X1C8,Y1C8X1,Y14#,80X1T,Y1H1G#4420:430:450]#5(YIYB)J1İ440x#665212,16813(X1C3)#>KEY(KB):SB,Z#@NXX1:KEYG1KEYG2KEYH7NXX1DX(X1G0)#CKEYG315000#HKEYC9KEYG0KEYG9NXX1DX(X1H1)$RZ "TH1"M$"CONCAVE MIRROR":CV0:CH12:10^"M$"< MOVE OBJECT LEFT":CH0:CV21:10"M$"> MOVE OBJECT RIGHT":10"M$"Q QUIT":10"M$"REAL":CH32:CV22.6:10:M$"VIRTUAL":CH32:CV21:10" 400:410: MIRROR + AXIS!#*X1,G8X1OR. NOTICE THE CONDITIONS THAT MAKE THE MOST ERROR"p!"BETWEEN THE CALCULATED IMAGE AND THE RAY DIAGRAM."!::"PRESS RETURN TO SEE THE PICTURE. ";:A$! CONCAVE MIRROR !XC180:J150:M21.533:X130:Y150:DX3.2:M5037:A.005":W:"YOU WILL SEE RAY DIAGRAMS FOR AN OBJECT IN FRONT OF A CONCAVE MIRROR." :"THE IMAGE POSITION IS CALCULATED FROM THE LENS EQUATION." :" 1 / F = 1 / D I + 1 / D O"7!:"THIS EQUATION IS SLIGHTLY WRONG FOR BIG OBJECTS CLOSE TO THE MIRRG4)KEYG315000@KEYC9KEYG0KEYG9NXX1DX(X1C5)UNXX1İ40:1200xZ:106:90:48:53:X170İ62X1124İ72300X1NX:THZ1Z1W:Z1H1Z1Z:1110: REPAIR LENS AND AXIS 1140l CONCAVE MIRROR G v::0BA$"1"ĺ"":1030:K CONVEX LENS MAIN CONTROL OL:3:1:0:X165tMX6279:Y6155:X477:Y42:80:40NM$"< MOVE OBJECT LEFT":CH0:CV21:10OM$"> MOVE OBJECT RIGHT":10PM$"Q QUIT":10QM$"CONVEX LENS":CH15:CV0:10188:G0172:G1190:G2174:G3209:G4131,X477:Y4T:G7275:TH3:G879:G9136:H0144:H18:H2139:H3141:H492:H512:H6255:H7149:H884-KB16384:SB16368.16368,0:A$:A$"5"ĺ:(4):"RUNMENU"0A$"3"25002A$"4"19008A$"2"300+&" 3 TO USE A CONVEX MIRROR."W'" 4 TO USE A CONCAVE MIRROR."w(" 5 TO END ";*Z0:W1:T2:XA140:C1278:C020:F1100:F2180:C260:YB80:C3130:C430:C55:DX2:Y150:X6279:Y6155:M234:C640:C7270'+C84:C91)(XX1)(X2X1)& #DE1D:DE:X:4 ':155:8^ '" ************************": $'" RAY DIAGRAMS: MIRRORS" .':" ************************" 8'255:I12000:::!B':30:"";:16368,0:A$:Z9111:L9(163 '#@(#2:30,60240,60:3:90,5790,63:132,57132,63-#CV8:CH11:M$" CC F":30:10:CV1:CH24:M$"CONCAVE MIRROR":102#A2.44:9184(A),6072(A):A2.44.60.04:9184(A),6072(A)::#S4:D30 #XX1X2S:X,Y1(Y2YAS":10:M$"INVERTED?":10:10060x\::6:Z$;", THAT'S IT FOR NOW. YOU"::"SHOULD WORK OUT SEVERAL MORE PROBLEMS":f"FOR YOURSELF. TRY PUTTING THE OBJECT"::"CLOSE TO THE MIRROR AND SEE WHAT OCCURS."p:"BYE FOR NOW!":20:10050z:"END"X1124:X2158:Y131:Y259:9100F66:X1118:X2240:Y149:Y249:9100q>5:147,59147,48145,51149,51147,48H10080:M$"SO THE VIRTUAL IMAGE IS REDUCED AND":10:M$"UPRIGHT. DID YOU NOTICE THAT THE REAL":10!RM$"IMAGE FROM THE CONCAVE MIRROR W10060 10080:M$"SINCE THE RAYS DO NOT CONVERGE, WE'LL":10:CVCV1:M$"LOOK FOR A VIRTUAL IMAGE AT THE POINT":10:CVCV1*M$"WHERE THE PROJECTIONS OF THE RAYS":10:CVCV1:M$"INTERSECT.":10:1006046:X1120:X2202:Y145:Y259:910056:1,30124,3094,410080:M$"RAY 3 WILL GO TOWARDS THE FOCUS. WHEN":10:CVCV1:M$"IT HITS THE MIRROR, IT WILL REFLECT":10:CVCV1:M$"BACK PARALLEL TO THE AXIS.":10:10060 5:51,30117,4970,4910080:CV18:CH9:M$"WHERE'S THE IMAGE?":10:LL REFLECT BACK":10:M$"WHEN IT HITS THE MIRROR.":10:10060R3:51,30120,4410080:M$"RAY 2 WILL GO PARALLEL TO THE AXIS.":10:CVCV1:M$"WHEN IT HITS THE MIRROR, IT WILL REFLECT":10:M$"AS IF IT HAD COME FROM THE FOCUS.":10:100601:5":30:10:10080:M$"HERE'S AN OBJECT IN FRONT OF A CONVEX ":10vM$"MIRROR. LET'S DRAW THE SAME RAYS.":10:1006010080:M$"RAY 1 WILL GO TOWARDS THE CENTER OF":10:M$"CURVATURE ":10:CVCV1:CH10:M$"(CC). ":30:10=CVCV1:CH17:M$"IT WI60,57160,63:202,57202,63cCV8:CH22:M$" F CC":30:10:CV1:CH24:M$"CONVEX MIRROR":10A2.44:20284(A),6072(A):A2.44.80.05:20284(A),6072(A):6:50,5950,3054,3446,3448,3248,3352,33@CV8::CH4:M$"OBJECTv3:112,61112,75:CVCV1nM$"THE TAIL OF THE ARROW REMAINS ON THE":10:CVCV1:M$"AXIS.":10:CVCV1M$"SEE HOW EASY IT IS, "Z$"!":10:1006010080:CV17:M$"NOW LET'S TRY A CONVEX MIRROR.":10:1006010070:2:30,60240,60:3:1?' 6e6- $$6 $6 tb$$ תܻe06'----ܻe eDDeEEIEee eDDeEEI H& X6&--.-%)266-)566>' --666%$$,666%$$,666R-? -666-e?-2-I166>?d-->?6-% 6o6- >? 8'666M!?5-I6666M )66-66 $$o6&66M!$?R-6? &->6&R-6>$-36R-.-$$5766M! I166?666M 666--.66M!$d 666n $ $$)66?$$-?066)6$$666M- ?)3-?--66&66- $$$66 $$666 $$$- ", $'5o M.$ $  6I66b1 ?.+-2--I)66?$$ >6-b-.-%b-o2?I.e 7&--.-6? 6- ?--6)?d=$)خ-?I--??b-)6o?56)256:233,Z9256:6[ +38=BJU]gr~ +5AMU^jq~$7BKS^ir#.>$-6 66n!1>6 5 X'< = 2D":10 +Z+:::5:"DO YOU WANT TO TRY ANOTHER MIRROR OR LENS? PRESS Y OR N. "h+:16368,0+:KEY(16384):KEY12815002+:16368,0:KEY128("Y")1060+:::2:"END"+:216,0+:,Z9(121)256(122):Z9Z973:232,Z9(Z9210? M$"THE LENS, IT DIVERGES AS IF IT HAD COME":CVCV1:10q M$"FROM THE FIRST FOCUS.":CVCV1:10:10060 1:43,24146,24200,2 10080:M$"RAY 3 GOES THROUGH THE SECOND FOCAL":10:CVCV1 !"M$"POINT. AFTER THE LENS IT GOES PARALLEL":11:M$"LET'S USE THE RAY METHOD...":10:10060f10080:M$"RAY 1 GOES THROUGH THE CENTER OF THE":10M$"LENS. RIGHT, "Z$"?":10:100603:43,24:Z9432502:Z9,(Z943)5620724:Z9 10080:M$"RAY 2 GOES PARALLEL TO THE AXIS. AFTER":IL3:("F")1202,57:("F")186,57:M$"DIVERGING LENS":CH23:CV2:106:42,2442,51:40,2644,26:46,2838,2842,2445,2739,2742,25CV7:CH3:M$"OBJECT":30:10CV14:M$"OUR OBJECT IS IN FRONT OF THE ":10-M$"LENS.":10:CVCV TYPE 2 TO CONTINUE.":10:16368,0>A$:A$"1"250wCVCV3:M$"NOW FOR DIVERGING LENSES... ":10:1006010070:2:30,52250,52:3:146,4146,100:147,4147,100:88,4988,55:204,49204,55:145,4145,100I010:141I,4151I,100:"VIRTUAL IMAGE.":10:10060c10070:CV5:M$"SO CONVERGING LENSES CAN PRODUCE BOTH":10:CVCV1M$"TYPES OF IMAGES, REAL AND VIRTUAL.":10:CVCV2M$"YOU CAN REVIEW OR GO ON.":10*CVCV1:M$" TYPE 1 TO GO BACK.":10:CVCV1:M$" 6+Z9521102:Z9,(Z952)32581:Z9TZ9501462:Z9,(Z950)30962:Z9oZ9501464:Z9,6:Z95:61,761,51:59,1063,1065,1357,1361,763,959,93:("I")58,5510080:M$"HERE WE HAVE AN UPRIGHT, ENLARGED":10:CVCV1:M$1,PM$"PARALLEL TO THE AXIS.":10:10060GX5:110,33146,6240,6Qb9000l10080:M$"SINCE THE RAYS DON'T INTERSECT, WE LOOK":10nCVCV1:M$"FOR A VIRTUAL IMAGE WHERE PROJECTIONS":10:CVCV1vM$"OF THE RAYS INTERSECT.":10:10060:1:112,33146,33242,65L<CVCV3:M$" CONTINUE . . .":10:10060D10080:M$"RAY 3 CANNOT GO THROUGH THE FIRST FOCAL":10:CVCV1FM$"POINT AND HIT THE LENS. WE DRAW IT AS IF":10NM$"IT HAD COME FROM THE FOCAL POINT, THEN":10:CVCV0:CVCV1:10060K3:111,33:Z91112161.5:Z9,(Z9111)5910533:Z9&10080:M$"RAY 2 IS PARALLEL TO THE AXIS. WHEN IT":10(M$"GOES THROUGH THE LENS, IT BENDS TOWARDS":CVCV1:10:CVCV10M$"THE SECOND FOCAL POINT.":10:CVCV1:10060343:1("O")110,58a M$"OUR OBJECT IS IN FRONT OF A CONVERGING":CH0:CV14:10:CVCV1M$"LENS, CLOSER THAN THE FOCAL POINT.":10:CVCV1:10060M$"RAY 1 GOES THROUGH THE CENTER OF THE":CVCV1:10:CVCV1M$"LENS UNDEFLECTED.":1- >? 8'666M!?5-I6666M )66-66 $$o6&66M!$?R-6? &->6&R-6>$-36R-.-?' 6e6- $$6 $6 tb$$ תܻe06'----ܻe eDDeEE.66M!$d 666n $ $$)66?$$-?066)6$$666M- ?)3-?--66&66- $$$66 $$666 $$$ H& X6&--.-%)266-)566>' --666%$$,666%$$,666R-? -666-e?-2-I166>?d-->?6-% 6o6I.e 7&--.-6? 6- ?--6)?d=$)خ-?I--??b-)6o?$$5766M! I166?666M 666--$7BKS^ir#.>$-6 66n!1>6 5 X'< = 2- ", $'5o M.$ $  6I66b1 ?.+-2--I)66?$$ >6-b-.-%b-o2?2191:0,Z9279,Z9:Z9:3:CH0:CV14:1":216,09"::F":"END":"Z9(121)256(122):Z9Z973:232,Z9(Z9256)256:233,Z9256:6[ +38=BJU]gr~ +5AMU^jq~36):Z9:(37)@!D'" ":!L'CH30:TVCV:CV23:M$"":10:16368,0:A$:Z915:L9(16336):Z9!N'0:Z9183191:210,Z9279,Z9:Z9:CVTV:!V':CH0:CV0:1:0:: HOME CURSOR, CLEAR SCREEN&"`'0:Z911CL$:@X,Y:N  37:$6 tb$$ תܻe06'----ܻe eDDeEE.-%)266-)566>' --666%$$,666%$$,666R-? -666-e?-2-I166>?d-->?6-% 6o6- >? 8'666M!?5-I6666M )66-66 $$o6&66M!$?R-6? &->6&R-6>$-36R-.-?' 6e6- $$6 M ?)36- -66?'$$--:066----:066)-5?$$666M!<-%$)66> I166?666M 666--.66M!$d 666n $ $$)66?$$-?066)6$$666M- ?)3-?--66&66- $$$66 $$666 $$$ H& X6&--$  6I66b1 ?.+-2--I)66?$$ >6-b-.-%b-o2?I.e 7&--.-6? 6- ?--6)?d=$)خ-?I--??b-)6o?$$5766M!$-6 66n!1>6 5 X'< = 2- ", $'5o M.$ 62AA21*PAA61AA13**ZAA94AA248*dCC$(AA)H*nII$II$CC$Z*s SET INVERSEk*xAA3260050*(CC$)30CH71,CV8:CHCH1:CH39CVCV1:CH0*60050**Z9(121)256(122):Z9Z973:232,Z9(Z9256)256:233,Z9256:6[27TTī60050)TT60260.)AA27ī60050Z) ESCAPE (27) = ALTERNATE CHARACTER SET)AA64AA91AAAA31:60260: CHANGE TO LOWER CASE) AA45AA95)AA47AA92)AA40AA91)(AA41AA93)2AA33AA27)":10:16368,0:A$:Z9111:L9(16336):Z9:%L'CH30:TVCV:CV23:M$"":10:16368,0:A$:Z915:L9(16336):Z9%N'0:Z9183191:210,Z9279,Z9:Z9:CVTV: &V':CH0:CVT TO":10:CVCV1>$zM$"THE FOCAL POINT.":10:CVCV3:10050I$15000O$'#$(#10080:CV17:CH9:M$"WHERE'S THE IMAGE?":10:CVCV1:10060:$'::144:8$'" ************************":$$'" RAY DIAGRAMS: LENSES"%.':" TO CONTINUE.":10%#bA$:A$"1"680[#f10070:CV5:CH0:M$"THAT'S THE END, "Z$".":10#hCVCV2:M$"YOU SHOULD DO SEVERAL MORE ON YOUR OWN.":10:CVCV1#pM$"EXPERIMENT BY MOVING THE OBJECT TO":10:CVCV1$rM$"DIFFERENT POSITIONS WITH RESPEC64:Z9,41:Z9A"R5:109,42109,51:105,46113,46109,42105,46c"TM$"IMAGE":30:CH14:CV7:10"\10080:M$"HERE IT IS; VIRTUAL, UPRIGHT, AND":10:CVCV1"^M$"REDUCED.":10:CVCV1#`M$"TO REVIEW THIS PROBLEM, TYPE 1.":10:CVCV1:M$"TYPE 2 0:CVCV1*!$M$"TO THE AXIS.":10:10060F!*5:43,24146,41230,41P!49000!>10080:M$"SINCE THE RAYS DIVERGE, WE FIND A":10:CVCV1!@M$"VIRTUAL IMAGE WHERE THE PROJECTIONS":10:CVCV1:M$"CONVERGE.":10:10060"H6:146,2592,49:Z99214uEu~` Eu@w@}aAx |Eu@@|?Eup@<` Eu`<EuP*A*AAEu|>@8`8``Eul?~@_s9``{w?pEu@{pEuEu0@809@Eu@C`qcg?`Eu@~~Eu@? Eu`;@A@Eժժժժժժժժժժժժժժժժժժժu`@|Eux}EupxF@ @Eu`3x@AEժժժժժժժժժժժժժժժժժժժu``\p@Eu@ ?`Eժժժժժժժժժժժժժժժժժժժus~n@9Eu@|`q Eu8xpE5U*U*U*U*U*U*U*U*U*U*U*U*U*U*U*U*U*UJu^``@p xEu@xp0< > px?EupEupF@0zEu`q8Eu`pppEu`p`@Eժժժժժժժժժժժժժժժժժժժu@C|?@|dpEu0@@~Eu|>@@pp`@~Dpg pEu@10s0@18N1 |{ `E}_+u`<`Eu8p@Eժժժժժժժժժժժժժժժժժժ>u``@?pEu@`s `Eu B>Eux@px `0Eu@0` pEu@wEժժժժժժժժժժժժժժժժժժժu|p`x`GEu@xp8`@L#|? EuEu` ` E5U*U*UjU*U*U*U*U*U*U*U*U*U*U*U*U*U*UJ+uEu@~00@Eu@>`A|Eu@`@@|Eu`^`@@EuCpEժժժժժժժժժժժժժժժժժժժu@A`<pEu p8Eժժժժժժժժժժժժժժժժժժժup@x@?xEu@ px``FsEu`|xp8 Eu?@<`CEUժժժժժժժժժժժժժժժժժ?up@Eu`@`x Eժժժժժժժժժժժժժժժժժժժux<p`>|@ Eu0@>?EuP*U* @aEu|@8@`l`XaEuxG?|Eժժժժժժժժժժժժժժժժժժժu@c@81|Eu `@@aEu<pp|p`p@`pEu@1F?sp @=paFb\|o@E}_+u~Eup Eժժժժժժժժժժժժժժժժժժժu`ppyxEup ` EuFA@`Eu<Gp|@x 0`Eu `@pB`@wpEu@EuEu~@xpppEu@xp`0`?@EuEu{|}prEu`q`qEժժժժժժժժժժժժժժժժժժժu`x8x@Eu0@0x@Eժժժժժժժժժժժժժժժժժժժu@cv`l}m~@Eu`@`pEu<`pxp@@3@<`pEu@18s0@0C?F#\|@E}_+u ~x@Eupp0Eժժժժժժժժժժժժժժժժժժժu```;pEu80@ EuCc0Eu<`p|ppEu `E0Bp@Eu@_?>E5U*U*U*U*U*U*U*U*U*U*U*U*U*U*U*U*U*UJu^``@p xEu@xp0< > px?EupEupF@0zEu`q8Eu`pppEu`p`@Eժժժժժժժժժժժժժժժժժժժu@C|?@|dpEu0@@~Eu|>@@pp`@~Dpg pEu@10s0@18N1 |{ `E}_+u`<`Eu8p@Eժժժժժժժժժժժժժժժժժժ>u``@?pEu@`s `Eu B>Eux@px `0Eu@0` pEu@wEժժժժժժժժժժժժժժժժժժժu|p`x`GEu@xp8`@L#|? EuEu` `.PR:"">#  " >#  @ @LY$Y$23:@@p```@ 0(23);C@/LD$;"@@    AL WAVE. K$I HO$;" I @ @J:">< "" >< "" @@ THE SAM8``8`P";SPZ@ @ @HZ:IG@" @20NTIN @"""" THE CUR  GqL1 " E`18: @@O CO(Y""@@ZD9 @   E>FVE I @ @ @L0C@@" "Y$(4) "@x"1:B "G WA OF B@ "OSE ONE.  @  B@ ""  @@@@TION                  u8(px6` 08Eu f``p@a`|3xx?zE}_+uEu p~@@Eժժժժժժժժժժժժժժժժժժժu px|p@<~xEu80Eua0Eu<|`<`hx`EuLC`Cq`~]?pEu@pEuEu~``@coEu@C|`~x@a>Eux}EupxF@ @Eu`3x@AEժժժժժժժժժժժժժժժժժժժu``\p@Eu@ ?`Eժժժժժժժժժժժժժժժժժժժus~n@9Eu@|`q Eu8xpEժժժժժժժժժժժժժժժժժժժu@c@81|Eu `@@aEu<pp|p`p@`pEu@1F?sp @=paFb\|o@E}_+u~Eup Eժժժժժժժժժժժժժժժժժժժu`ppyxEup ` EuFA@`Eu<Gp|@x 0`Eu `@pB`@wpEu@EuEu~@xpppEu@xp`0`?@EuEu{|}prEu`q`qEFC?BEGIJJJHFC?<841/---.0259<@CFHJJJIGDA=:630.---/147;>BEGIJJJHFC?<841/---.0259<@CFHJJJIGDA=:630.---/147;>BEGIJJJHFC?<841/---.0259<@CFHJJJIGDA=:630.---/147;>BEGIJJJHFC?<841/---.0259<@CFHJJJIGDA=:630.---/147;>BEGIJJJHd`]ZXVUUUVXZ]`cfiloqrrrqpnkhea^[YWUUUUWY\_behknprrrrpnlifb_\YWVUUUVX[^adgjmoqrrrqomjgd`]ZXVUUUVXZ]`cfiloqrrrqpnkhea^[YWUUUUWY\_behknprrrrpnlifb_\YWVUUUVX[^adgjmoqrrrqomjgd`]ZXVUUUVXZ]`cfiloqrrrqpnkhea^[YWUUUUWY\_behknprrrrpnlifb_\YWVUUUVX[^adgjmoqrrrqo  u` E5U*U*UjU*U*U*U*U*U*U*U*U*U*U*U*U*U*UJ+uEu@~00@Eu@>`A|Eu@`@@|Eu`^`@@EuCpEժժժժժժժժժժժժժժժժժժժu@A`<pEu p8Eժժժժժժժժժժժժժժժժժժժup@x@?xEu@ px``FsEu`|xp8 Eu?@<`CEUժժժժժժժժժժժժժժժժժ?up@Eu`@`x Eժժժժժժժժժժժժժժժժժժժux<p`>|@ Eu0@>?EuP*U* @aEu|@8@`l`XaEuxG?|p@<` Eu`<EuP*A*AAEu|>@8`8``Eul?~@_s9``{w?pEu@{pEuEu0@809@Eu@C`qcg?`Eu@~~Eu@? Eu`;@A@Eժժժժժժժժժժժժժժժժժժժu`@|V D1P1:D2P2:D3P3:D4SRHV 6000RV 7000XVuV*** STANDING WAVE ***VIN$;CL$V7:"1. EXPLANATION OF STANDING WAVE "V:"2. FAST DEMONSTRATION "V:"3. RETURN TO MAIN MENU "W::"... "2. FAST BEAT DEMONSTRATION "EU :"3. SLOW BEAT DEMONSTRATION "gU :"4. RETURN TO MAIN MENU "U ::"... CHOOSE ONE ... ";:Y$U Y$:NM$U (Y$)1(Y$)43000U (Y$)3100,3200,3300,100U NZ$"SUP.1":16025U! 23:39:Y$:3000"DES.5":16025T16368,0+T23:38:Y$9TSC$:100?TZTl3098:I0300:3276:`TvfT}TNZ$"DEF.1":16025T16368,0T23:39:Y$T100T *** SUPERPOSITION ****T IN$;CL$T 5:"1. EXPLANATION OF SUPERPOSITION "U :"PRESS... ";:16368,0"SY$(SS"THE VELOCITY OF THE WAVE IS V. ":"THE EQUATION WHICH LINKS F AND 1L0 IS 1L0 = V/F . "S16368,0SY$S(25);WR$SNZ$"DES.4":16025S16368,0S23:38:Y$ TNZ$"= 1/PERIOD OR F=1/ T ."RRZ02500:Z:J010:"";:I116:3266:Z08:Z,I,JkR"PRESS A KEY... ";yR16368,0RY$R:"ANGULAR FREQUENCY IS MEASURED IN RADIANS PER SECOND. THE SYMBOL IS OMEGA ( 1W 0). 1W0 = 21P0 F . "SOD = T "Q~Z02500:Z:""CQI116:3266:Z075:Z,I:""fQ"PRESS A KEY... ";:16368,0nQY$Q:"THE FREQUENCY IS THE NUMBER OF WAVE- LENGTHS THAT PASS A GIVEN POINT IN ONE PERIOD OF TIME. THE SYMBOL IS F. "R"FREQUENCY ,120136,120:J,I(Pi0:72,120136,120DPn16:14:"1 L0 ";HO$RPq16368,0uPs9:"...PRESS A KEY... ";:Y$PxCL$;"THE PERIOD OF THE WAVE IS THE TIME THAT IT TAKES FOR THE WAVE TO TRAVEL THROUGH A DISTANCE OF ONE WAVLENGTH. " Q}:"PERI2,120 ORZ08OUX72136:X,12040(4AZ):ZZ1:XOZ2:"ONE WAVELENGTH IS THE DISTANCE ALONG THE X AXIS BETWEEN IDENTICAL POINTS. "O_:"THE SYMBOL MOST OFTEN USED TO DENOTE WAVELENGTH IS LAMBDA ( 1L0 ) ."PdI045:J07:J:72" N#1335N2"CORRECT"NN7:"...PRESS ANY KEY TO CONTINUE... ";:Y$N<CL$;"THE FOLLOWING DEFINITIONS ARE IMPORTANT AND SHOULD BE MEMORIZED."::"...PRESS A KEY... ";:Y$NA(25);CL$:9:40:(23)NF1:0,120255,120NK3098OP0:7E.  ":"PRESS ANY KEY TO TRY AGAIN. ";:Y$;MCL$:1275M"WRONG. REMEMBER THAT SIN0=SIN1P0=SIN21P0=0 ":"PRESS ANY KEY TO TRY AGAIN. ";:Y$:CL$:1275NCL$:"YOU ARE GUESSING (AND NOT VERY WELL)":"THE CURVE IS DESCRIBED BY Y = SINX .SINX (B) SIN2X (C) SIN21P0X (D) COSX "_L:" X IS IN RADIANS. "::"CHOOSE ONE... ";:Y$pLCL$:FLFL1L Y$"A"1330LFL3FL0:1310LY$"D"1305,MY$"D"ĺ"NO, A COSINE HAS A MAXIMUM VALUE AT X=0. THIS CURVE IS OBVIOUSLY A SIN138,130138,170'K202,130202,170=K23:19:" X=0 "ZK23:18:" X=21P0 "uK23:28:" X=41P0 "K23:9:" X=0 "K10:9:" Y "K9:40:(23);CL$KFL0K1(L"WHICH OF THESE DESCRIBES THE WAVE ":"BELOW? ":"(A) ȠŠΠŮӠ٠٠ϠŮǠԠŠӍΠӠՠŠĠϠōҠˠĠŠŠԈӠȠŠŠΠčӧΠȠΠϠӠƍԠ٠ŠĠǍײ΍ϠҠŠӠƠŠŠōĠŠŠΈΠŠŠΠٍ̠ԠӠŠ͠ƠŠӮӠӠĠήԠӍϠĠŠŮŠ  "c~3c0,130"cX02554:cX,16030(AX2)fc2:" PLOTTING COS 1D0K/2 "mcXc2:" 1A0 = COS 1D0K/2 "c0,160:""cX02552cX,16030(9.5AX)d3:" PLOTTING SIN(K110+K12);"BLOAD DENSE.SINES.1""bb(16)jbg8:38:"Y1":13:38:"Y2":19:38:"Y1":20:39:"+":21:38:"Y2"bi1:"Y110=SIN(K110X - 1W10T) Y120=SIN(K120X - 1W20T) "bl3098:3110:3122bqI1255bv3184:3220:3256b{Ic}"A$"S"DEDE5 aA$"I"60901aA$"M"6200Ja23:20:IN$;SP$;NM$~aDE1DE1:23:20:IN$;"MAXIMUM SPEED ";NM$a16368,0a6030aY$:Y$"I"6030aD4:6090a8D440024000aBD440613000aX***** BEATS *******b](4. S":"SINGLE STEP... I":21:20:"MENU.... M";NM$D`D1:D2:D3`5:38:"Y1":10:38:"Y2":14:38:"Y1":15:39:"+":16:38:"Y2"`D4:I1DE:I`(16384)1276045`6030`A$((16384)128)`16368,0`A$"F"DEDE5aTO TRY AGAIN... ";:Y$:5400`_1NM$;CL$:5300:5360:22:7:"...PRESS ANY KEY.. .";:Y$:5000{_p*** STANDING WAVE ***_s(16)_t2:0,40255,40:0,80255,80:0,120255,120_uDE50_z20:IN$;CS$:4`21:"FASTER........ F":"SLOWER.......R505425^.:"YOUR AMPLITUDES ARE TOO LARGE. THE SUM OF THE ABSOLUTE VALUES OF THE ALL THE AMPLITUDES MUST NOT BE GREATER THAN 50. "::" ALSO, RELATIVE FREQUENCIES MUCH BIG- GER THAN 10 DO NOT PLOT VERY WELL. "_0::"...PRESS ANY KEY 0" ]]IN$,CL$::"]R0R]" AMP FROM -20 TO +20, FREQ. FROM .5-50":]I15:"AMPLITUDE FOR WAVE ";I;"....";:20000:CO(I)(Y$)]""RELATIVE FREQUENCY FOR WAVE ";I;"....";:20000:FR(I)(Y$)]$]'I:I15:RR(CO(I)):I ^, \14:CS$ \21:37:"SUM";H\0,140:X02554:X,140AM%(X):XO\I^\X02554k\AM%(X)0r\Xx\\3:37:FR(1)\1:30:"REL.FREQ. "\6:37:FR(2)\8:37:FR(3)\11:37:FR(4)\13:37:FR(5)]18:37:"1S.75:FR(1)3:FR(2)9:FR(3)15:FR(4)21:FR(5)27:CL$:5300:5360E[[I15:CO(I)8:I:I15:FR(I)6I:I:CL$:5300:5360[[[3:I15[0,20I:X02554[Y20ICO(I)(AFR(I)X)[AM%(X)AM%(X)Y20I[X,Y:NN1[X(Y$)ZWNM$ ZZR1R352056Z_R5260,5250,5270DZ`16368,0jZa23:7:"PRESS ANY KEY... ";:Y$tZd5000ZCO(1)20:CO(2)10:CO(3)5:CO(4)2.5:CO(5)1.25:I15:FR(I)3I:I:CL$:5300:5360Z?[CO(1)18:CO(2)6:CO(3)3:CO(4)1.5:CO(5)05YR5100,5200,5400,5080&Y100=YNZ$"COM.1":16025TY23:39:Y$:(10)^Y5005qYP*** DEMO ****ZUIN$;CL$:" YOU MAY LOOK AT... ":::"1. SQUARE WAVE "::"2. SAWTOOTH WAVE "::"3. WAVE PACKET ":::" CHOOSE ONE... ";:Y$:RES ***XIN$;CL$3X" COMPLEX WAVES "QX:::"1. EXPLANATION "WXqX"2. DEMONSTRATION "wXX"3. YOUR FREQUENCIES "XX"4. RETURN TO MAIN MENU "X::" CHOOSE ONE... ";:Y$XR(Y$):R15005YR450CHOOSE ONE ... ";:Y$:Y$4W(Y$)1(Y$)34000=WNM$VW(Y$)4100,4200,100lWNZ$"ST.1":16025|W 23:39:Y$WNZ$"ST.2":16025W23:39:Y$:4000WhD1P1:D2P2:D3P3:D4SLWr(13);(4);"BLOADSINES"W|6000X*** COMPLEX WAVϠӮӈЈӠ٠٠ϠŮΠŠΠȠӍĠŠנŠϠ٠ǍӠŠϠ͠ǠŮŠԠӠĠŠōРՈŠϠ٠ԠŠوĭǠŠӠ٠Š͠ƠŠҍ .<&( <*(6$ 0($ $1"$*$ "8$ $$ #)-*8  80,>c""""?""?""?>k>?""">""""  "c6**"""&*2""""""""?!!?""?""?6c"""""k*"">> >00000>"**     >> """   > ">> """>""""""< >> "ĂQU"jNQU4J$"CORRECT":20230>jNQU2J$"CLOSE":20230MjOJ$"WRONG"SjOj0uCL$::"SORRY...THERE'S BEEN AN ERROR... ":j5u(222)255ĺ"DON'T PRESS THAT KEY!!!"j:uZ01000:Z:7"2:uZ01000:Z:7(AN$)8200005i4N(AN$)8Y$(Y$,(Y$)1):20005Ji9NAN$(13)20040Xi>NY$Y$AN$ciCN20005iiHNiN" PLEASE CHECK YOUR SPELLING AND RETYPE":"THE ANSWER... ";:iN*** CHECK AGREEMENT ***iNQU1(Y$)jN((Y$,QU,1))((AN$(I),QU,1));NZ$h>(16)h>1:!h>1454h>D$;"OPEN";NZ$Gh>D$;"READ";NZ$Nh>I`h>J1I:A$(J)kh>A$(J)h>(A$(J))1āJJ1555:JJh>Jh>255h>D$;"CLOSE";DZ$h>h NY$""h!NZE(0)h%NAN$:AN$;h*NY$""(AN$)820005i/N(Y$)2:**** READ KEYBOARD ****$g;A$""Dg;KB(16384):KB12715140[g;A$(KB):16368,0ag$;og<3:0,100|gD$(13)(4)h>"FILE NAME"L SHAPED ":AN$(4)"ERROR ":AN$(5)"SINE ":AN$(6)"COSINE "ZfQ'A23.141592255nfV'WR$(15)(23)f['SC$(15)(19)fs'f:A23.141592255f:I04f:AD4096I256f:X0255f:ADX,20(I1)4((4I)AX)f:Xf:If:g(1):P2$(15)(2)FL1CE?20:CS$:1060EB18:CS$:18:" NO...IT IS USUALLY CALLED A GAUSSIAN ":"CURVE. ":1120EGZ01000:ZEL F`18:CS$:18:" IT IS SOMETIMES CALLED A GAUSSIAN, A":"BELL SHAPED, OR AN ERRORIT CALLED? ";:20000;D&(Y$,5)"CURVE"Y$(Y$,(Y$)5)FD.I14dD020200:J$"CORRECT"1080yD1J$"CLOSE"1080D3I:D4J$"WRONG"D8"";J$:Z01000:ZD9FL1J$"CORRECT"1090E:J$"CLOSE"Ģ20:IN$;CS$:20:20100:Z02000::20$ C CL$KC1:" HERE IS A TRAVELING WAVE IN THE SHAPE OF A PULSE. "UC1900C18:" DO YOU KNOW WHAT THIS FUNCTION IS ":"USUALLY CALLED? ";:20000CFL0C(Y$,1)"N"ī1100C(Y$,1)"Y"ĺ"":18:CS$:1045D$20:" WHAT IS 000,2000,3000,4000,5000,200%B32995BNZ$"DES.1">BWR$IB16025WB16368,0gB23:38:Y$~BNZ$"DES.2":16025B16368,0B24:38:Y$B1:BD$;"BLOAD DENSE.PULSE.1"BNZ$"DES.3":16025B16368,0B24:38:Y$CSC"3. SUPERPOSITION OF WAVES (INTERFERENCE)"GA"4. STANDING WAVES"MAgA"5. COMPLEX WAVES "mAA"6. QUIT ":A16368,0A20:"CHOOSE ONE... ";:Y$:Y$:"... ONE MOMENT PLEASE ... "A(Y$)1(Y$)6100ANM$B(Y$)1* @6147@30000#@A$(25)0@1012,69;@ 10000P@ A23.141592255W@3l@d**** MENU *****y@nIN$;CL$@x" MENU"@}ZE(0)@255@::"1. EXPLANATION OF SIMPLE WAVES"@@"2. DEFINITIONS "@-A             WAVES STARTER" , [WHICH DO YOU WANT ? ";, P16368,0:A$: Z16368,0H dA$"5"Āz nA$"1"ĺ(13);(4);"RUN MIRROR RAY DIAGRAMS" xA$"2"ĺ(13);(4);"RUN LENS RAY DIAGRAMS" A$"3"ĺ(13);(4);"RUN LENS AND MIRROR EXPERIMENT" A$"4"ĺ(13);(4);"RUN  ::-" OPTICS PROGRAMS"S::"PRESS THE NUMBER YOU WANT:"{(::" 1. MIRROR RAY DIAGRAMS"2:" 2. LENS RAY DIAGRAMS"F:" 3. LENS AND MIRROR EXPERIMENT"H:" 4. WAVES"K:" 5. QUIT" M::"  "*:<"">""""""""""""">>><2"<""">""" ""  ">"6**"""""&*2""""""""""""*,"" "" ">""""""""""""""**6"""""""> >>> >00000>">>>< (&20 *, **>> "2*&" " >>  ">> "8""> """"""< >> "$$>A]E]A>AAIAI~DD~ P"""A>*""@@  |*((6>6>"6*">88>>>>*>><> ?:{> 8p`p8  |x||||`p8||`8 c1 0cF0`@|WUEE}zj@@LR^B\@**EEEUW|@`0Fc0 1c 8`~BBzzB? !!//!!!!! ?BBBB~x||  || |~?>~|\xx| ||x0000~~0000p` ?? |x 8p`@  Ll< <"<"""<< <"""<"><$""< """"  "" 6***""""""""""<""< :< $"""2,"""""**6"""""< >>8  8"*:<"">""""""""""""">>><2"<""">""" ""  ">"6**"""""&*2""""""""""""*,"" "" ">""""""""""""""**6"""""""> >>> >00000>">>< (&20 *, **>> "2*&" " >>  ">> "8""> """"""< >> "$! $%%#,fp% "Lp"% $`"H *+)hi#"H !*0+i+idH#d hd`"%$$%H hi#`$% c,d*+Me,dPMc*!0 +i+`%J) b+je *`PPPP򠥹͠0tL"$!e (' !!%##`f`" e$$ ",r0st(!#L"L $b .  %   `L a,gPgA[8 & & &mh)mi e$*+Me$(Mc,dp ,cpP!pA* +i+Me$rs"t`,Tb@0,U`* L" {LB$!$$"% %L"c`g`g`,,Lҩc`@a`de` qLXde`s$t%L$td`e`g`f`Yd`e`L$e (' 8!$!$%",rL !%# "L5 )5`)aW L| JHIHa`G~#+@HPXs{GG+R$a`1  emhi` b` ,r0rbj$s%t`@b`s$$hLde`,rSjbLL  L%L% C `u8967 ,R,W U ,P`ɭӠҠΠΠ ((*)  b+*HN OI*P,h*,H,`0ɛ` ɍ $h`ɐ 6+` qL L { :::255.6:" W A V E S"O:::20:"COPYRIGHT 1981"p(:20:"DR. PAUL STEPHENSON"220:" PLEASE WAIT A MINUTE."<(4);"EXEC AUTO" %71C3T,84:6873,H8:68YB,H8:G CONCAVE MIRROR CENTER RAY uX0T:X3C1:M0(YBY1)(XCX1):X1C3422Y3YB(X3XC)M0:Y3H1X3XC(X3XC)(YBC8)(YBY3)Y0YB(XCX0)M0:Y0Y6X0XC75M0:Y0Y6X1,Y1XC1,YBX0,Y0:X1C3ıXI,YBWXI,YIXITH,YJXITH,YJXI,YI774XIT,H8:S DRAW CONCAVE MIRROR ~162,20: START DRAWING CONCAVE MIRRORYC0H3H1:XCA(YYB)T,Y:Y DRAW AXIS FOR CONCAVE MIRROR T,YBC1,YB:YB,YBTYB,YBT:C3,YBTC3,YBTlX1,Y1X4,YIY1,YI0mXX4H6C8:X,YI:X:Oq AXIS FOR CONVEX MIRROR prW,YBC7,YB:F4,YBTF4,YBTs71F4T,H8:68G7,H8:68269,H8:{ IMAGE FOR CONVEX M |XIXCJ1(XCX1)(F4X1)~YIYB(XIXC)(YBY1)(XCX1):YJYITH%Y3Y1(YBY1)T:X3XC(XCX1)T<\X1,Y1XC,YBX1,YBYBY1a]XXCX3TH:X,YB(XXC)M0:X:^X1,Y1185,Y1G6,0: CONVEX MIRROR RAY COMING IN PARALLEL`XW45TH:185X,J1XM:X:g CONVEX M, TOWARD F hX4F4(F4X1)(YBYI)(YBY1)THE TYPE OF IMAGE ,,654883(XIXA),136F-654883(XIXA),144h.654883((YIYB)C4),156:J DRAW CONVEX MIRROR K198,C0:Y25H2H1:XCA(YYB)T,Y:Y:V CONVEX M, THRU CENTER WM0C4(XCX1)YY3Y1:X3XCXCX1:X3C7G3,Y73XF1XAC8:X,Y7:X:: DOTTED EXTENSIONN CONCAVE LENS IMAGE nXIXAC6(XAX1)(C6XAX1)YIYB(YBY1)(XAXI)(XAX1)YJYIC8XI,G8XI,YIXIC8,YJXIC8,YJXI,YI: ARROW74XITH,H4:: LOWER CASE 'I'+ PRINT M1(X3X1):Y3H3X3X3C0:1443X1,Y1X3,Y3:b IN PARALLEL, OUT F FOR A CONCAVE LENS yX1,Y1XA,Y1X6,Y6XX4XA3:X,Y4(XX4)M2:X: IN F, OUT PARALLEL FOR A CONCAVE LENS Y7Y1(Y1YB)(XAX1)(F2X1)X1,Y1XA,Y7l74XITH,YBH5((XIXA)(XIXA)):LABEL 'I'fmXI,YKXI,YIXIC8,YJXIC8,YJXI,YI:: DRAW ARROWw DRAW CONCAVE LENS xI08:G9I,C4H0I,C3:I:H2,C4H2,C3H3,C3H3,C4} RAY THROUGH CENTER M1C4(XAX1):X3C1:X0T Y3Y180X1T,H4:Gc GET IMAGE POSITION XI, YI FOR CONVEX LENS MdxfXIXA(XAX1)C6(F1X1):XIZXIG7ıhYIYBC4(XAXI)(XAX1):YIZYIY6ıiYJYIC8((YIYB)(YIYB)):YKYB(XIXA)(XIXA)jXIDXXIG7ıkYIWYIG0ı.AXIS ( PW,YBC1,YB:220,YBT220,YBT= QF2,YBTF2,YBT] R71F1T,YB4:71F2T,YB4 SF1,YBTF1,YBT:C2,YBTC2,YB2 T2054,84:7161,84:20214,84:71221,84: Y DRAW OBJECT ARROW ZX1,G8X1,Y1X1C8,Y1C8X1C8,Y1C8X1,Y1\M2Y4:X:, ; IN THROUGH F OUT PARALLEL O <M3(YBY1)(F1X1):YAYBM3C6h >X1,Y1XA,YAC1,YA: E IN F, OUT PARALLEL WITH DOTTED EXTENSION FM3(Y1YB)(X1F1):YAYBC6M3 HX1,Y1XA,YAC1,YA JXTXAC8:X,YA:X: O DRAW ENSION IF X1 LEFT OF F1 (REAL IMAGE) Q /Y0Y1M1(X0X1):Y0WX0X0H1:47k 0X1,Y1X3,Y3:X1F1ı 1M0C4(XAX1):XX0X1TH:X,Y0M0(XX0):X: 2 IN PARALLEL, OUT THROUGH F 5X1,Y1XA,Y1X6,Y6 6X1F1ı 7XX4XATH:X,(XX4)G9,YB:142,YBXA,C4138,YBXA,C3H3,YBXA,C4H2,YBXA,C3143,YBXA,C4137,YBXA,C3142,YB| )143,YBXA,C3:142,YBXA,C3: * RAY THROUGH CENTER +M1C4(XAX1):X3C1:X0T ,Y3Y1M1(X3X1):Y3H3X3X3C0:44 -X1F148) . NO DOTTED EXT L8(Z):CHZ:CVCVW:9  CONVERT M$ TO LOWER CASE e HH$(M$,1): CHANGE M$ TO LOWER CASE L8T(M$):L9((M$,L8,W)) L964L991L9L931 !HH$HH$(L9):L8 "M$HH$: ' DRAW CONVEX LENS Z (H0,YBXA,C4G9,YB:H0,YBXA,C3X(:1000: LENS EXPERIMENT COPYRIGHT 1981 BY MARK CROSS\ PRINT STRING M$ AT CH,CV m TH:L9(M$) L8WL9:L7((M$,L8,W))C4 X9CH7W:Y9CVH1 L7T14:Z:65X9,Y9:TH:15L7X9,Y9CHCHW:CH39CHZ:CVCVWL8              95,77:CVCV1:M$" THIS RAY REFLECTS PARALLEL TO THE":10:M$" AXIS.":10:10060b10080:CV18:CH9:M$"WHERE IS THE IMAGE?":10:10060l10080:M$"THE TIP OF THE ARROW IS AT THE POINT":10:CVCV1:M$"WHERE THE THREE RAYS INTERSECT.":10:1006010:100607:10080:M$"LET'S DRAW RAY 2.":10:10060D1:51,30165,30:165,3199,89:CVCV1:M$" THIS RAY REFLECTS BACK THROUGH THE":10:CVCV1:M$" FOCUS.":10:10060N10080:M$"FINALLY, DRAW RAY 3.":10:10060TX5:51,30171,77:171,77TO CONTINUE: ";:10080:A$:A$"1"Ĺ16297,0:16299,0:16304,0:44016297,0:16299,0:16304,0:M$"NOW LET'S SEE HOW THIS WORKS...":10&M$"HERE COMES RAY 1.":10:10060 03:51,31153,108:CVCV1:M$" THIS RAY REFLECTS BACK ON ITSELF.":"3 - A RAY FROM THE OBJECT THROUGH THE":CV17:10:M$" FOCAL POINT REFLECTS BACK":CVCV1:10M$" PARALLEL TO THE AXIS.":CVCV1:10:10060::10:"DID YOU WRITE DOWN THE THREE RAYS?"::"IF NOT, TYPE 1 TO SEE THEM AGAIN. TYPE":F"2 " THE CENTER OF CURVATURE. IT REFLECTS":10^M$" BACK ALONG ITSELF.":10:10060:CVCV1M$"2-A RAY FROM THE OBJECT POINT PARALLEL":10:M$" TO THE AXIS. IT REFLECTS BACK THROUGH":10M$" THE FOCAL POINT.":10:10060:CVCV1a10080:M$AGINE THE OBJECT ON THE RIGHT":10:M$"OF THE MIRROR AND YOU WOULD HAVE A":CVCV1:10M$"DIVERGING (CONVEX) MIRROR.":CVCV1:10:1006010080:M$"HERE ARE THE THREE SPECIAL RAYS:":10:CVCV1-M$"1-A RAY FROM THE OBJECT POINT THROUGH":10:M$.";:10050M10070:CV19:M$"HERE'S WHAT WE MEAN . . . ":10:10060:100709000:6:50,5950,3054,3446,3448,3248,3352,33CV8:CH5:M$"OBJECT":30:10M$"HERE'S AN OBJECT IN FRONT OF A CONCAVE":CV15:10CVCV1VM$"MIRROR. IME OUT.";:10050::r"> THE RADIUS OF THE MIRROR EXTENDS FROM"::" THE CENTER OF CURVATURE (CC) TO THE"::" MIRROR.";:10050:: |"> THE FOCAL POINT (F) IS LOCATED ON THE"::" AXIS OF THE MIRROR HALF WAY BETWEEN"::" THE (CC) AND THE MIRROR50::]J"FORTUNATELY WE NEED NOT DRAW IN ALL"::"POSSIBLE RAYS. AS WE'LL SEE, ";Z$;",":T"THREE RAYS ARE ENOUGH.";:10050^:"HERE'S WHAT YOU NEED TO KNOW ABOUT"::"MIRRORS:":h"> CONCAVE MIRRORS CURVE INWARD: CONVEX"::" MIRRORS BULG3:"TO FIND THE LOCATION OF THE IMAGE POINT"::"USING THE RAY METHOD, WE SIMPLY DRAW IN": 6"THE RAYS SHOWING HOW THEY WOULD BE"::"REFLECTED. THE IMAGE IS AT THE POINT":@"WHERE THE REFLECTED RAYS (OR THEIR"::"PROJECTIONS) INTERSECT.";:10010050::c "WHEN THE RAYS STRIKE A MIRROR, THEY ARE"::"REFLECTED AND CONVERGE AT A POINT TO"i  "FORM AN IMAGE."::"IF THE RAYS DON'T CONVERGE THEN THERE": ""IS A VIRTUAL IMAGE WHERE THE EXTENDED"::"RAYS COME TOGETHER.":10050\ ,:AND COMPASS TO MAKE YOUR OWN DRAWINGS."::O "WHEN YOU'RE READY...";:10050 :"IN THE RAY MODEL FOR LIGHT WE ASSUME"::"THAT LIGHT RAYS DIVERGE FROM EACH POINT": "OF AN OBJECT. THE RAYS STREAM OUT UNTIL"::"THEY STRIKE A MIRROR OR LENS.";:S YOUR NAME? ";Z$::n "THANKS, ";Z$;"! IN THIS PROGRAM"::"WE'LL LOOK AT THE RAY DIAGRAM METHOD FOR" "FINDING THE SIZE AND POSITION OF IMAGES"::"PRODUCED BY CONCAVE AND CONVEX MIRRORS."::+ "YOU'LL PROBABLY WANT A PENCIL, RULER,"::":CVCV1:5 HH$(M$,1): CHANGE M$ TO LOWER CASEV L82(M$):L9((M$,L8,1))p L964L991L9L931 !HH$HH$(L9):L8 "M$HH$: d- RAY DIAGRAMS: MIRRORS i24576:63999 k15000 n:10000 :3:"HELLO, FRIEND!"::"WHAT'4100: MIRRORS BY STEVE KAMM AND MARK CROSS ` 3:L9(M$): PRINT STRING M$ AT CH,CV L81L9:L7((M$,L8,1))30 X9CH71:Y9CV8 L7214:0:65X9,Y9:3:15L7X9,Y9CHCH1:CH39CH0:CVCV1L8 L8(0):CH0          ,100:88,4988,55:204,49204,55`148,16148,88:149,40149,60:145,16145,88:144,40144,603:("F")188,59:1("F")205,59:CV2:CH23:M$"CONVERGING LENS":106:110,33110,51:108,35112,35114,37106,37110,33113,36107,36109,34111,1>M$"REMAINS ON THE AXIS. THE IMAGE IS REAL.":10:1006010070:CV9:M$"NOW LET'S SEE WHAT HAPPENS WHEN WE":10:CVCV1M$"PLACE THE OBJECT CLOSE TO THE LENS.":10:CH0:CVCV2:10060 10070:2:30,52250,52:3:146,4146,100:147,41479,53239,82:237,79241,79235,76243,76241,80237,80237,79241,79242,77236,77237,78241,78CV5:CH32:M$"IMAGE":30:1010080:M$"THE TIP OF THE ARROW IS FOUND AT THE":10M$"INTERSECTION OF THE RAYS. THE TAIL":CVCV1:CH0:10:CVCVES THROUGH THE FIRST FOCAL":10\M$"POINT. WHEN IT PASSES THROUGH THE LENS":CVCV1:10M$"IT BENDS PARALLEL TO THE AXIS.":CVCV1:10:CVCV1:100605:43,24139,83253,83M$" AGAIN.":CVCV2:CH22:10:A$9000`5:2310:10060F|10080:M$"RAY 2 IS PARALLEL TO THE AXIS. AFTER IT":10|~M$"PASSES THROUGH THE LENS IT BENDS TOWARDS":10M$"THE SECOND FOCAL POINT.":10:100601:43,24139,24249,89:M$"HERE IT IS.":CVCV1:10:1006010080:M$"RAY 3 GO10:CVCV1:100601h10080: ERASE BOTTOM TEXTkjM$"RAY 1 GOES THROUGH THE CENTER OF THE":10:CVCV1lM$"LENS UNDEFLECTED.":10:CVCV1r3:43,24:Z943253.8:Z9,(Z943)6320924:Z9: HPLOT43,24TO252,87 SLOWLY tM$"CONTINUE . . .": LENS":10PJ6:42,2442,51:40,2644,26:38,2846,2842,2440,2744,2742,24rTCV7:CH3:M$"OBJECT":30:10YM$"OUR OBJECT IS IN FRONT OF A CONVERGING":CV14:10:M$"LENS.":10^CVCV1:10050`CVCV1:M$"NOW LET'S APPLY THE RAY METHOD.":"Z$:10.10060]610070:2:30,52250,52:3:138,4138,100:88,4988,55:188,49188,558139,10139,94:140,20140,84:141,35141,659137,10137,94:136,20136,84:135,35135,65 @3:("F")183,59:("F")1191,59:CV1:CH0:M$"CONVERGINGGO THROUGH A DIVERGING LENS.":30:10:CH0:CVCV2:10060~"10070:CV7:M$"WE'LL BE USING TWO FOCAL POINTS":30:10:CVCV1$M$" (EQUIDISTANT FROM THE LENS)":30:10:CVCV1&M$" AND NO CENTER OF CURVATURE.":30:10:CVCV3,M$"HERE WE GO, G THREE SPECIAL RAYS.":30:10:CVCV1:10050n CVCV1:M$"YOU SHOULD ALREADY KNOW THAT LIGHT RAYS":30:10 CVCV1:M$" TEND TO CONVERGE AFTER PASSING THROUGH":30:10:CVCV1 M$" CONVERGING LENSES AND THEY DIVERGE WHEN":30:109M$" THEY Y . . .":CVCV2:10 10060b 10070:CV2:M$"WE'LL USE THE RAY MODEL OF LIGHT THAT":30:10 CVCV1:M$" WAS DESCRIBED IN THE MIRRORS PROGRAM.":30:10:CVCV1 M$"WE'LL USE THE SAME IDEA FOR FINDING":30:10:CVCV1- M$" IMAGES - DRAWIN FOR":10> M$"FINDING THE SIZE AND POSITION OF IMAGES":10 CVCV1:M$"PRODUCED BY CONVERGING AND DIVERGING":10:CVCV1 M$"LENSES. YOU SHOULD ALREADY HAVE SEEN:":10 M$" 'RAY DIAGRAMS: MIRRORS'":CVCV2:10 M$"WHEN YOU'RE READ63999: SET UP START OF APPENDED SHAPE TABLEI CV1:M$"HI THERE!":10q CVCV2:M$"WHAT'S YOUR NAME? ":10 CH19:CVCV1:60000: INPUT Z$ CVCV2:M$"THANKS, "Z$"! IN THIS PROGRAM":10 CVCV1:M$"WE'LL LOOK AT THE RAY DIAGRAM METHODCV1:0 HH$(M$,1): CHANGE M$ TO LOWER CASEQ L82(M$):L9((M$,L8,1))k L964L991L9L931 !HH$HH$(L9):L8 "M$HH$: d- RAY DIAGRAMS: LENSES i24576: ABOVE HGR2 k15000 n10000: PRINT TITLE x10070:3:1:0- <'1100: LENSES BY STEVE KAMM AND MARK CROSS\ 3:L9(M$): PRINT STRING M$ AT CH,CV} L81L9:L7((M$,L8,1))30 X9CH71:Y9CV8 L7214:0:65X9,Y9:3:15L7X9,Y9CHCH1:CH39CH0:CVCV1L8 L8(0):CH0:CV           C?<BEGIJJJHFC?<841/---.0259<@CFHJJJIGDA=:630.---/147;>BEGIJJJHFC?<841/---.0259<@CFHJJJIGDA=:630.---/147;>BEGIJJJHFC?<841/---.0259<@CFHJJJIGDA=:630.---/147;>BEGIJJJHFC?<841/---.0259<@CFHJJJIGDA=:630.---/147;>BEGIJJJHFqqwwvUvuutsrqpnlkhfdb_]ZXVTSQPPPPPQSTVXZ]_bdfhklnpqrstuuvvvwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwww ` ` ` ` ``  `}`   0 P p    0``   0  p    0`>" <<77..%%:>P#P'P+P/P3P7P;P?#'+/37;?`L \ ~()(-(1(5(9(=!%)-159=("(&(*(.(2(6(:(>"&*.26:>(#('(+(/(3(7(;(?#'+/37;?P P$P(P,P0P4P8P< $(,048"&*.26:>#'+/37;?#'+/37;? $(,048< $(,048"&*.26:>#'+/37;?#'+/37;? $(,048< $(,048"&*.26:>#'+/37;?#'+/37;?   ](?(?`@ L`        WAVES STARTER" , WHICH DO YOU WANT ? ";, P16368,0:A$: Z16368,0H dA$"5"Āz nA$"1"ĺ(13);(4);"RUN MIRROR RAY DIAGRAMS" xA$"2"ĺ(13);(4);"RUN LENS RAY DIAGRAMS" A$"3"ĺ(13);(4);"RUN LENS AND MIRROR EXPERIMENT" A$"4"ĺ(13);(4);"RUN  ::-" OPTICS PROGRAMS"S::"PRESS THE NUMBER YOU WANT:"{(::" 1. MIRROR RAY DIAGRAMS"2:" 2. LENS RAY DIAGRAMS"F:" 3. LENS AND MIRROR EXPERIMENT"H:" 4. WAVES"K:" 5. QUIT" M::"  ӠȠΠōĠŬŠ٠Ԡ٠ŠƍŠӠԠŮԠӬǠŠԠՠ΍Ԡ٠Ӯؠՠ٠נŠŠ͠ĠԠĠԠ٠ӮԮӠ٠Š٠˽Я́ӠĠōŠƠŠŠҮŠŠԠϠŠŠǠōŠΠӠ͍ٽفρΨؠׁԩՠĠ٠ԠӠӠΠō͠ٽ٨حԩŠŠŠ  T,,P(x(J"l"EbB\AZB\EbJ"l"P(x(U--Z22]55^66]55Z22U--O'v'I!j!EbAZAZB\EbJ"l"P(x(V..[33^66^66]55Z22U--O'v'I!j!D`AZAZB\FdK#n#P(x(V..[33^66^66]55Y11T,,N&t&I!j!D`AZAZB\FdK#n#Q)z)V..[33^66^66]55Y11   .V(PHF&K/S1Yֲ֤ؾŧڭѬԽܲľĦD(p((6z(( a((n((a((y(( p((6q(( z((b((n((`((y((7p((7q(({((c((n((`(( x((6(( q((|((c((n(( `((6g((((q((|((d(((FGN&W/Y1U+M"FG"N,V1Y Ġ֠ӠȈŠĠƠŠŮӠӠԠŠŠ΍ĠҠƠӮŠƍŠ̠ŠĠΠŠԠŮӠ٠٠ϠŮϠנӠΠΠͭŠӮΠǠԠƠŠٍƠŠŠΠĈӠԠ٠ȍΠƠŠ͠ƽƨحԩӠΠϠŠŠ̠ōήΠӠΠؠӍҠԠӠŲ٠ΠȈȍӠŠŠΠӍŮԠӠϠԠҍŠ̠ŠΠ̠ōΠ̠ӮΠҭǠƠӠΠӠԠčΠҠ   wwwwwwwvvvuutsrqpnlkhfdb_]ZXVTSQPPPPPQSTVXZ]_bdfhklnpqrstuuvvvwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwww Ҡ٠ׁנЁƍĠԽƍ́֯Ơׁ֠ˠ֠ŠčӠو٠٠ϠŮĈӍȠ́ŠŠ΍̠ӠΠŠŠԮ٠ƽŠҠƍӠȠӠԍΠŠԠƠŮŠҠ˽Ё́  Ԡ٠ō̠ӠŠҠōŮҠΠҠōΠҠǠĠԠوȠӍԠŠ٠ԠȠӠƠŠǮӠ٠٠ϠŮٽحԍٽحԩحԩٽШحԩٽΨحԩٽӨحԩȨحԩ̠ƠŠӠŠӍƠŠŠ׈ήŠԠ͠ƠŠΠҠҠŠ̠ Š٠˽Я́ӠĠōŠƠŠŠҮŠŠԠϠŠŠǠōŠΠӠ͍ٽفρΨؠׁԩՠĈĠو٠ԠӠӠΠō͠ٽ٨حԩŠ ٠ǠƁŠ҈Šզ֘հְհԝհ_12 eij졠믽ذض۴ij̸̺ᥭ̵̿˸ʶ̸ܸݸݕݸָٸĠŠŠԠƍŠŠΠ  ōŭŭŭŭűűűĠȮύΠӍӠ٠٠ϠňӠ٠٠ψϠŮĠԠÈàŠӠȠӠҠΠӮӈ̠̠Ġ̠ΈŠĠȠ̠٠ϠōӠĠŮӠ٠٠Ϡ٠ԍӠƠƈǠ͠Šύ٠٠̠ŠňŠŠ̠ԭӠΠϠ̠ӮҠӠΠŠԠȠӠ̍ŠĠĠ̮Š̠ŠԲŠӍŠԠƠ׈ӠӠԠύ٠ӠƠӮ̠ɈŠ҈Ӡ͠ΠԠԠƠŠو٠Ơȍ̠ĠΠӮȠŠ   ̠ŠĠΠŠԠŮӠ٠٠ϠŮ̠ōήΠӠΠؠҔ̠ҠԠӠŠĠ֠ӠȈټĠƠŠŮƈӠӠԠŠŠΠԈͭĠҠĈƠӮŠƠŠ  !!  {x""