+JJJJ  X/ lӠˠӠϠӠϠԮԠҠˠčӠ٠ϠԮ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,&"_]` L/浍굺L  !"#$%&'()*+,-./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#0EB 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݌`HIHHHHhHH݌hHhHh݌H6 VDP (ED Z $0x8x D- ܸDD# H8`?E Vk *f???0xE Hh D#-EEE8` D ܸx D - ܸx8`-0ݩ?ʥD EEE`   vLDcpq` [` ~  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 ?L>>";::1:A$:24:1:" )1281B50200_BF(0):Q1(232):Q2(233):232,0:233,8:Q3(249):0:Q4(231):1:XZXXB100XX,YY:(WD$)LāQ1(WD$):((WD$,Q,1))31:99::232,Q1:233,Q2:Q3:Q4:BLTRL11:X$(WD$,LTR,1):X$(32)X$"-"ĂcCW$(WD$,LTR(X$C,IT:QXI,Y:sAIT98:SC,RIT:RT,A:QUI,U:SC,IS:RT,W:QUI,U:SC,RIT:RT,A:QUI,U:SC,IS:RT,WBQUI,U::X97:Y114:I050:SC,MIS:RT,O:QXI,Y:SC,IQ:RT,B:QXI,Y:SC,MIS:RT,O:QXI,Y:SC,IQ:RT,B:QXI,Y::(49152;@1002:32767:864,1:865,0:866,4:867,0:868,5:869,0:L45:3:1:0:"BLOAD SHAPES,A$175D":232,93:233,23:"BLOAD SQUEEZE,A$9577":2000AX48:Y64:49:A:I246:RT,A:SC,RIT:QXI,Y:RT,N:SC,IT:QXI,Y:RT,A:SC,RIT:QXI,Y:RT,N:S                      uUUW`G]]]_UUUWꪪ:**+8G{;;;>***+UUU^@EwU***+pEn~***+uUUU\D]}Uz***/`p`D@>xpp`?8(?8888 8t^*<R;;?**UW`PwwUU^j+8Pnnn~**uU^@N]]]}UU_:*+pN;;;z**/UU\Mwww}UUWj*/`Lnnnz**/uUUxK]]]uUUWꪪ:**.@J{;;;j**+UUWpIwUUUWꪪj**<Innno***+@U`?@Ux W@~YpY@V |Q@;+WO" wUzxP@nn*WT ]]U~*pV;;*_Vwu*pVnnz+=_V]]uU/h T;;j*Ux@PwwuUޫj.@Pnnoj*uWpR]]_UUj*+0Jnnn~***uUU\J]]]}UUUު:**+H{;;;z***UUUXHwuUUUުj**.Fnnnoj***uUUUF]uUUU^z***,E{;j***UUUWDwU_*8p\|[`\xUWk<Onn~*+uVO]]]UW+0O;;>*+U\Sww}UUj+Qnnnz*+uUXQ]]]uUU:*.O;;;j*+UUOwwwUUUj*,Nnnno***uUWM]]]_UUU:**8L;;?***UUVKwwwUUUa[\[USRP M I+ Fn D]/ F;u IwU/ Mn*UM]WU~/M;?*/uNw   spectrometer. The brightness also goes down as the order increases.)":YYYY10:15hwGw100:BACK30480wLw:WD$"The grating you are using is called a ''replica grating.'' It is made by pouring plastic over a master grating.":YY10:15:300xVwWD$"A you to very accurately measure the angles. Then you can work ''backwards'' and find the wavelengths.":YYYY20:15:300SwBwWD$"(You probably won't be looking at anything more than second order diffraction since the angles get too large to see with the 30450u.w:WD$"Sending different colors or wavelengths into the grating will result in a whole series of diffraction angles. Each wavelength will go off at a different angle, given by that last equation.":YY10:15:300yv8wWD$"The spectrometer allowslength":XX40:YY90:5:100,85130,40:300:WD$"Grating Line Separation":XX100:YY120:5:150,40140,113:300u$wWD$"Diffraction Angle":XX180:YY70:5:185,40195,66:300:WD$"You should have already seen this equation in class.":YY130:15:100:BACKs would give 3 .":YY110:15:940,129:100:BACK30390sw:WD$"In the general case (for any desired diffraction order):":YY10:15:WD$"n = d sin":XX120:YY30:5:9126,29:10178,29:300ntwWD$"Order":XX30:YY50:5:70,53115,33:300:WD$"Wave B @` @ : @@@@ @242@34224#@@ @@@@+P BPP1 @@ @@ C(0`  x@x@x@x@x8 ? pp ? pp ? pp ? <<<<<@ @@@ @@@@ ĄDŽĎ$%ЈЈа2CA`aDxxxxxĂĂćĂć𠈂à    " = d sin":XX120:YY30:5:9123,29:10177,29:300rvWD$"If we did the same thing with the second order diffraction wavefronts the opposite side of the triangle would be 2 .":YY60:15:9190,89:3009swWD$"The third order diffraction wavefront30:249,R48:150,30:I190::150,30:249,R:150,30:::232,93:233,23:0:1qv10100,50:1080,20:T120:B140:200:WD$"See why the angles are the same?":YY120:15:100:BACK302307rv:WD$"We can rewrite the equation this way:":YY10:15:WD$0@i vX10327017:X,160X64,0::0:Y1040:75,Y250,Y::3i*vWD$"d is the distance between slits.":XX85:YY20:5:WD$"d":XX2:YY117:5:5,1005,110:5,1305,140:0,10010,100:0,14010,140:100:BACK30200,j4v0:Y1040:75,Y275,Y::3:WD$"Tigure it out, let's look at the first order case again. Remember, there is exactly one wavelength difference between circles.":YYYY20:15h v100:BACK30160iv:0,50:1,145:38263:20,11040,160:20,7055,160:20,3072,160:22,088,160:40,0103,1620:YY20:L25:5:L45*gu100:BACK30130gu:WD$"We need an equation giving us the diffraction angle of the wavefronts. (In other words, what is the angle between straight ahead and the actual motion of the wavefronts?)":YY10:15:300hvWD$"To f160:X,12665,Y:X,10685,Y:X,85105,Y:X,65125,Y:X,45145,Y:X,25165,Y:X,5185,160guX20527020:X,160X170,0::0:Y1066:110,Y200,Y::3:WD$"These wavefronts move off at a steeper angle. (Order = 2, wavelets differ by two cycles.)":XX1f at an angle. (Order = 1, circles differ by one cycle.)":L30:XX85:YY20:5:L45:100:BACK30110eu0,50:1,145:38263: HPLOT 20,110 TO 40,160: HPLOT 20,70 TO 55,160: HPLOT 20,30 TO 72,160: HPLOT 22,0 TO 88,160: HPLOT 40,0 TO 103,160XfuX20:Yh front.)":L30:XX90:YY20:5:L458du100:BACK30070du0,50:1,145:38263:20,11040,160:20,7055,160:20,3072,160:22,088,160:40,0103,160duX10327017:X,160X64,0::0:Y1070:75,Y250,Y::3eeuWD$"This group of wavefronts moves of":XX86:5:95,135125,123/cu100:BACK30050Gcu0,50:1,145:38263cu31,031,160:45,045,160:X6127015:X,0X,160::0:Y1066:80,Y260,Y::3#duWD$"This group of wavefronts moves straight toward the right. (Order = 0, same circle for eacYY2:5:20,595,5:WD$"Slits in Grating":YY27:5:20,5895,30:WD$"Wavelets":YY54:5:70,7095,57cuL20:WD$"Each radius increases by one wavelength.":XX130:YY100:5:L45:232,93:233,23:0:1:979,125:78,14090,140:WD$"<":XX77:YY137:5:WD$">e lines or scratches) act as sources of wavelets. If you could actually see them it would look like this....":YYYY10:15:100:BACK30000avu::10:10:"GETTING THE GRATING....":"BLOAD GRATING,A$9132":0,50:1,145::38263dbuWD$"Grating":XX100:Xu100:BACK2000`bu:WD$"Imagine you are looking down on a grating (like an overhead view of a picket fence). There is light of a single wavelength coming in from the left.":YY10:15:300aluWD$"The slits of the grating (the smooth part between thin your spectrometer.":YYYY10:15:300_NuWD$"When mounted properly, wavefronts from the collimator land squarely on the grating. Each slit then acts as a source of circular waves. (They are actually cylindrical in three dimensions.)":YYYY10:15`so that they can diffract light waves. There are often as many as 10,000 slits per centimeter of grating!":YY10:15(_Du300:WD$"There are two different types of gratings, transmission and reflection. You will probably be using a transmission grating sn't diffracted.":YY120:5:68,60150,60:146,57150,60146,63Tpv100:BACK30230pvT120:B140:200:WD$"Watch the top vertex of the triangle.":YY120:15:300pv232,96:233,3:40:249,60:149,29:249,0:150,30RqvJ110:R6064:249,R:150,:15:100:BACK30200rov:50,3050,10080,8550,30:WD$"d":XX35:YY62:5:965,98:76,7869,8372,88:1052,51?pvWD$"This is the direction of the wavefront.":YY10:15:68,60150,28:142,28150,29146,34:300:WD$"This is where it would go if it wayour equipment is quite delicate and certainly expensive. Use care when working with it!":YYYY10:15:100:BACK10340](2000]/u]0u GRATINGSv^:u::WD$"A grating acts as a great number of parallel slits. These slits are very close together (100:BACK10220\(:WD$"You will probably enjoy using a spectrometer. It is fairly simple to operate, yet gives very precise measurements. Besides--you get to look at all the pretty colors!":YY10:15:300x](WD$"You must remember, however, that you will be using.":YY10:15:300[n(WD$"If it is a degree scale with a vernier you should be able to measure angles to 1/10 of a degree. If you don't know how to do this, run the lesson on vernier calipers. The scales are similar.":YYYY10:15\xr will have some kind of scale to allow you to read the angle of the telescope.":YY10:15:100:BACK10210$[d(:WD$"There are many different types of scales that are used on spectrometer bases. You will have to talk to your instructor to see what typeYP(LAST30:150:1180,110:16:195,105:163,115:WD$"These shields are placed over the grating or prism to block stray light from entering the telescope.":YY10:15:100:BACK10210lZZ(LAST30:150:195,105:163,115:WD$"The base of the spectromete0:15:100:BACK10210X<(LAST30:150:1110,90:32:1180,110:WD$"This is the fine adjustment for the telecope position. Once the scope is locked in place, turn this knob to center the crosshairs on the spectral line."XF(YY10:15:100:BACK10210m deviation), this knob is tightened.":YY10:15:60,50130,80TW((100:BACK10210X2(LAST50:150:0:60,50130,80:3:115,74120,72:0:1110,90:WD$"This knob locks the telescope into position once you have a spectral line near the crosshairs.":YY1inside it, slide just the eyepiece in or out.":YY10NV (15:100:BACK10210iV(LAST30:150:1200,50?W(WD$"This tiny knob is the table lock. Once the grating is perpendicular to the light beam (or if using a prism, it is set at the angle of minimu the brightness of the spectral lines and how wide they appear.":YY10:15:100:BACK102105V(LAST20:150:150,63:16:1200,50:WD$"The telescope is focussed on the slit by sliding the whole tube in or out of its support. To focus on the crosshairs be similar in operation.":YY50:15:100:BACK10060zT'::10:15:"STAND BY...":"BLOAD DETAILED SPECTROMETER,A$9177"T'0,119:1,145::38263T'232,0:233,21:0:1:150,63\U'WD$"This little knob adjusts the slit opening. With it you controlle attached to the base of the spectrometer. That's all there is to it!":YY100:15iS'100:BACK100304T':WD$"Let's take a closer look at a typical spectrometer. The one you are using may have the controls in different places, but it will probably e telescope can be moved along an arc until the color you want is centered on its crosshairs.":YY100:15~R'100:BACK10030TS'T110:B160:200:WD$"Once the telescope has been carefully aimed at the desired wavelength, the angle is measured from a sca00:36,2492,18:36,2492,32140,32:92,18140,18177,35:140,32170,50Q'177,35220,80:170,50225,70260,83:222,80260,97:100:BACK10030iR'T110:B140:200:WD$"Each different wavelength or color comes out of the grating at a different angle. Th15:100:BACK10030P'T110:B140:200:WD$"Let's mount a grating on the table. It must be adjusted until it is perpendicular to the rays coming from the collimator.":YY100:15:300GQ'140,12140,10138,10138,42140,42140,40:Y42122:140,Y::3e":XX180:YY44:5:WD$"hypotenuse":XXXX6:YYYY12:5:170,53245,53:300nvWD$"sin =":XX120:YY100:5:10138,100:9172,94:WD$"d":XX174:YY106:5:170,103183,103:300ovWD$"It turns out that this angle is also the diffraction angle.":YY120prism or a grating.":YY100:15:100:BACK10030O'T110:B140:200:WD$"Telescope":XX220:YY30:5:215,36210,45:WD$"The telescope is focussed on the slit and makes it easy to measure the angle associated with a particular beam of light.":YY100P'has a lens positioned a focal length away from the slit. This produces parallel rays (or ''columns'') of light.":YY100:15Nt'100:BACK100300O~'T110:B140:200:WD$"Table":XX175:YY0:5:160,10172,3:WD$"The table has a clamp which holds either a 40:200:WD$"Slit":XX22:YY50:5:32,4732,38:WD$"This slit lets light into the spectrometer. It is often adjustable to different widths.":YY100:15:100:BACK10030|Nj'T110:B140:200:WD$"Collimator":XX50:YY70:5:70,6770,38:WD$"The collimator PLE SPECTROMETER,A$9177":0,119:1,145:38263LV'WD$"Light Source":YY10:15:15,815,13:WD$"Here is the source of light. It isn't actually part of the spectrometer, but you couldn't get much done without it!":YY100:15:100:BACK10030M`'T110:B1ers can use either a grating or a prism. You will have to ask your instructor as to which you will be using. (Maybe even both!)":YYYY10:15:300KB'100:BACK10000-LL':WD$"Let's look at the main parts of all spectrometers.":YY10:15:"BLOAD SIM100:BACK1000J.'L46::WD$"As you have already learned in class, it is fairly easy to split light into its different colors or wavelengths. A spectrometer lets you take measurements of these wavelengths.":YY10:15:300:L45K8'WD$"Most spectromettice that it is a right triangle.":YY120:15:76,7869,8372,88:100:BACK30200mvLAST19:150:T130:B140:200:WD$"Using trigonometry, we can easily find this angle.":YY10:15:1052,51:300KnvWD$"sin =":XX120:YY50:5:10138,50:WD$"oppositust the distance between two wavelets, one wavelength.":YY100:15:10,10529,75elpv100:BACK30200lzv:WD$"Let's enlarge the triangle so that we can see it easier.":YY10:15:50,3050,10080,8550,30:WD$"d":XX35:YY62:5:965,98:300QmvWD$"NoYX14,Y39::X2135:21,37X,72::20,60:35,7270,72:36,71k\vX10327017:X,160X64,0::0:Y1040:75,Y250,Y::3:21,7334,68Plfv232,93:233,23:1:0:WD$"Now that we've gotten rid of all the extra lines....":YY10:15:300:WD$"This was jhis is also d, only shifted.":XX85:YY20:5j>vWD$"d":XX2:YY48:5:T32:B72:0,T10,T:0,B10,B:5,T5,T10:5,B5,B10:100:BACK30200jHv0:Y031:0,Y279,Y::Y73160:0,Y279,Y::?kRv21,3073,160:22,088,160:40,0103,160:Y32:X2362:X,I'WD$"Before making any adjustments to your spectrometer, check with the instructor. It takes a long time to get everything set properly. Don't waste valuable lab time resetting adjustments that were already done for you in advance."J$'YYYY10:15:000,30000,50000,1000H':L44::WD$"Spectrometer measurements are among the most precise you will make in an intro-ductory physics lab course. Since these devices are so sensitive they require special care when they are used.":YY10:15:300H'L45 WHAT IS YOUR CHOICE? [ ]"::" (NO NEED TO PRESS 'RETURN')":21:31:A$GA$"1"A$"2"A$"3"A$"4"ĺ(7);(7):::9:"PRESS ONLY 1,2,3, OR 4!";:2030G" ":" "G21:31:A$:22:1:958:23:12:"PLEASE STAND BY..."H(A$)10 ":5:" SPECTROMETERS ":5:" ":F9:10:"1. USING THE INSTRUMENT"::10:"2. HOW GRATINGS WORK"::10:"3. HOW PRISMS WORK"::10:"4. RETURN TO EQUIPMENT MENU"PG1:21:" "PLEASE STAND BY... ...GETTING THE MENU!":1023,1:"VERIFY MAIN MENU"zE1023,6:216,0:"RUN MAIN MENU":E:10:"I CAN'T FIND THE MENU. INSERT DISK A AND PRESS A KEY.":A$:" ":1010E:: MENUdF:5:" 4:5:YTY1TY1:TX1,YTX1,Y::0D DELTADTX,TY:TX1,TY1:TX2,TY2:TX3,TY3:TX4,TY4:TX4,TY4:TX3,TY3:TX2,TY2:TX1,TY1:D1500D::10:"PUT IN SIDE A OF THE FIRST DISK AND PRESS A KEY.":A$:" ":SE::10:10:7):102 Cn C ERASE WORDS FC0:Y0LAST10:0,Y279,Y::3:fC0:ETB:0,E279,E::3:yC,ZZ12000::CZZ11000::CX +- SIGNCbTX,TYTX,TY4:TX2,TY2TX2,TY2:TX2,TY6TX2,TY6:C  DOTS$D*WD$"o":XXTX2:YYTY ARROWS AND ESCBeBACK0Bf49168,0:24:958:24::4:"<<< LEFT OR RIGHT ARROW OR ESC >>>";::1:A$:24:1:" ";BhA$""ĺ" "::2000BjA$""BACK1:" ":BkA$""ĺ" ":Cm21:1:958:(7);(D$):((WD$,Q,1))31:99::232,Q1:233,Q2:Q3:Q4:jALTRL11:X$(WD$,LTR,1):X$(32)X$"-"ĂAW$(WD$,LTR(X$(32))):100XX,YY:QQ1(W$):((W$,QQ,1))31:99::WD$(WD$,(WD$)LTR):99:XXXZ:YYYY10:6AXX0:YYYY10:5:Bd :@1002:37169:864,1:865,0:866,4:867,0:868,5:869,0:L45:3:1:0:"BLOAD SHAPES,A$175D":232,93:233,23:"BLOAD SQUEEZE,A$9577":2000@F(0):Q1(232):Q2(233):232,0:233,8:Q3(249):0:Q4(231):1:XZXX5A100XX,YY:(WD$)LāQ1(W                                        how to make a graph of index versus wavelength.":YYYY10:15:300{BWD$"Time to return to the menu!":YYYY30:15:100:BACK50930{Lǫ1000:X,Y:YY1:{&Y110:X1122403:X,Y:YY1::Y102:X1421683:X,Y:YY1:A|22:"theta =";TH:THTe prism. This is necessary because the index of refraction does not change uniformly or linearly with wavelength.":YY10:15:300B{8WD$"If you need to make these corrections your instructor will supply you with standard wavelengths and information on $"A":XX138:YY80:5yY110:X1122403:X,Y:YY1::Y102:X1421683:X,Y:YY1::WD$"D":XX200:YY100:5:200,95200,93198,90195,85:200,110200,112198,115195,120y$ǰ100:BACK50890z.Ǒ:WD$"This equation is often used to ''calibrate'' th5:XX160:YY43:5:WD$"A + D":XX170:YY15:5:WD$"2":XX182:YY27xư5:YYYY26:5:WD$"A":YYYY11:5:145,38202,38:170,24200,24:180,50188,50xǓ140,70185,14095,140140,70:0,150112,110165,110250,145:245,140255,150:245,150255,140yWD`p0@p;p`|;p `}=x  @@=G$b0@@8  @@Zp>B8p|` |8@x@|` 8?pp~ ~@<@`  ``x|D:`8`'?'  8~~8 /|: aa` :@p `a`:p? ?? ?;?< < <䤧=<]]PX]%8h`YxZ`@^@A@a8ZZA@q@89@@@8;ψ[Ј8`9<``; '' | ||||~| (?=   he incident index of refraction equal to 1. We will also rename the other index...."::YY100:15:100:BACK50620BxƑ:WD$"At the angle of minimum deviation:":YY10:15:WD$"n =":XX95:YY32:5:WD$"prism":XX105:YY37:5:WD$"sin":XX150:YY20:@]A( Y  ! @O@@P JBB  !A@H ` @ AKDH *(" xxxxxx0 DED|3  | G EpppppppHa @]"D@X@@@ R  P@J$-@ @" H@ # K(0@ETA xx0@*"|4 ? |UEpI  B!@Rx @Q  @Q0 `Q `Q@  Q@ 0R `@ 0J8R @0@0U }Q R R Q QࠐRU`\ 0 Xb@bXX((((xV$@0  Q  `L`<K_`8`M`@ @0R @``W@ azi 0 XB2BXWx((((xUU U U U U U U U"㢜P L__KN R``WƣR܋Q   1150,35:1236,35:232,93:233,23:WD$"i":XX78:YY55:5:WD$"r":XX187:5vWD$"A + D":XX118:YY45:5:WD$"A":XX228:5:WD$"2":XX130:YY57:5:XX228:5:115,54150,54:225,54235,54:300rwWD$"Assuming that the prism is in air allows us to set tives:":YY10:15:WD$"n sin = n sin":XX100:YY20:5:WD$"i":XX108:YY25:5:XX145:YY25:5:WD$"r":XX171:5:XX208:YY25:5:10135,20:10198,20:300KvWD$"n sin = n sin":XX70:YY50:5:232,0:233,22:32:1112,73:1222,73:0:Y35:5:WD$"A + D":XX70:YY25:5:WD$"2":XXXX12:YYYY10:5:68,33100,33tƔ10170,30:WD$"r":XX180:YY35:5:WD$"=":XX190:YY30:5:WD$"A":XX200:YY25:5:WD$"2":YY35:5:199,33205,33tư100:BACK50600uƑ:WD$"Plugging into Snell's Law gz#?@*    ӠР=ĠӠ!+ Ӡ<Ҡ٠KŠͮà ĠҮà" ͮà" ͠ŠҠĠҠ ӠŠҮàϠӠĠ;ŠǠԠǮà"77:YY34:5:WD$"i r":XX102:YY50:5:WD$"=":XX126:YY40:5:80,43115,43:140,43182,43:300]WD$"Now we define a material's INDEX OF REFRACTION, n, as the ratio of the speed of light in vacuum to the speed of light in the material.":YY7115,123:140,123182,123:100:BACK50340[đ:WD$"After cancelling out the hypotenuse we arrive at:":YY10:15:WD$" sin sin":XX80:YY30:5:WD$"v v":XXXX15:YYYY15:5:10103,29:10168,29j\WD$"i":XX113:YY34:5:WD$"r":XX1onometry gives:":YY70:15:WD$"Hsin Hsin":XX80:YY110:5:WD$"v v":XXXX15:YYYY15:5:10103,109:10168,109)[WD$"i":XX113:YY114:5:WD$"r":XX177:YY114:5:WD$"i r":XX102:YY130:5:WD$"=":XX125:YY120:5:80,123WD$"v v":XXXX8:YYYY3:5:96,13113,13:133,13152,13YWD$"We have used a ''v'' for the speeds. Don't forget that the subscripts mean incident and refracted.":YY30:15:300ZWD$"Calling the common hypotenuse H, and applying a little trig"speed":XXXX8:YYYY13:5:125,93180,93Xİ300:WD$"Since the times for both sides are equal....":YY130:15:100:BACK50180>Yđ:WD$"time = =":YY10:XX50:5:WD$"d d":XXXX50:YYYY10:5:WD$"i r":XXXX8:YYYY3:5:YYYY15:5:e distance d as it did for the other edge to go d .":YY10:15zWWD$"i":XX140:YY35:5:WD$"r":XX117:YY44:5:300*XWD$"Solving speed = distance/time for time gives:":YY50:15:WD$"time =":XX80:YY90:5:WD$"distance":XXXX50:YYYY7:5:WD$ngles have a common hypotenuse. Copy this drawing if you haven't already.":YY10:15:100:BACK50130AWđ:WD$"Even though the two sides of the beam were moving at different speeds, it took exactly as much time for the right edge of the beam to travers50:WD$"Let's label the two different distances travelled by the two sides of the beam.":YY10:15UWD$"d":XX150:YY50:5:XX90:YY90:5:WD$"i":XX158:YY55:5:WD$"r":XX98:YY95:5:100:BACK50130gVLAST20:150:WD$"Also note that the two tria0:BACK50130T|LAST26:150:WD$"These angles are equivalent.":YY10:15:1093,65:WD$"i":XX103:YY72:5:10132,82:WD$"r":XX142:YY88:5:100:BACK50130cUĒ0:WD$"Original Speed":XX150:YY45:5:WD$"Slower":XX40:YY100:5:3:75,102:LAST1:1hĒ0:Y3039:90,Y110,Y::181,80217,160:3:Y301403:75,Y::232,93:233,23:1:0:1058,55:1080,120:WD$"i":XX68:YY60:5:WD$"r":XX90:YY125:5 TrLAST20:150:WD$"We will designate these as the incident and refracted angles.":YY10:15:10$"Now both sides of the beam are in the water and travel with the same reduced speed.":YY10:15:Q1oROİ300RTX97:Y114:I050:SC,MIS:RT,O:QXI,Y:SC,IQ:RT,B:QXI,Y:SC,MIS:RT,O:QXI,Y:SC,IQ:RT,B:QXI,Y:R^İ100:BACK50130S10:15:WD$"Slower":XX40:YY100:5:WD$"Original Speed":XX150:YY45:5:Q1VQ;İ300Q@āIT98:SC,RIT:RT,A:QUI,U:SC,IS:RT,W:QUI,U:SC,RIT:RT,A:QUI,U:SC,IS:RT,W:QUI,U:QCē94,114180,80QEİ100:BACK50130fRJLAST20:150:WD:QXI,Y:RT,N:SC,IT:QXI,Y:RT,A:SC,RIT:QXI,Y:RT,N:SC,IT:QXI,Y:uP1ē75,80107,40:100:BACK50130MQ6LAST20:150:WD$"Now the left side of the beam enters the water and slows down. The right side continues at the original speed.":YY:WD$"AIR":YY60:15:WD$"WATER":YY75:15:Q15Oī1SOĹ49168,0:100:BACK50130O"LAST16:150:WD$"Before it touches the surface, all parts of the beam travel with the same speed.":YY10:15:Q1O'İ300RP,X48:Y64:49:A:I240:RT,A:SC,RIT:X1122403:X,Y:YY1::Y102:X1421683:X,Y:YY1::WD$"D":XX200:YY100:5:200,95200,93198,90195,85:200,110200,112198,115195,120:100:BACK50600\m*LAST40:150:WD$"Notice that this angle is half of angle D. We will label it with the l:15:100:BACK50600k LAST20:150:WD$"Let's label the angle between prism sides with the letter A.":YY10:15:WD$"A":XX138:YY80:5:300kWD$"Also look at how we define the angle D, the deviation from the unrefracted path.":YY20:15l Y1107,65177,15075,135147,65:0,15092,118168,125240,158jŒ3:140,70185,14095,140140,70:0,150112,110165,110250,145:LAST20:150kWD$"If you watch through the telescope while twisting the prism, you can set this angle quite accurately.":YY10s spread out into the familiar spectral pattern.":YY10:15eŰ300:WD$"Let's look at a prism with a beam of white light going into it from the left.":YYYY20:15:100:BACK50550fʼn::10:10:"SETTING UP THE PRISM....":"BLOAD PRISM,A$8000":0,0:r words, different colors slow down by different amounts."\dYYYY10:15:100:BACK50500LAST20:150:WD$"We should also put in the incident and refracted angles for the 150112,110165,110250,145:245,140255,150:245,150255,140:100:BACK50600hLAST50:150:WD$"If the prism is turned from this position, the beam is refracted through a greater angle.":YY10:15`iŒ0:140,70185,14095,140140,70:0,150112,1101he ANGLE OF MINIMUM DEVIATION. By rotating the prism you will find a position where the light is bent the least. At this point the beam inside the"NhYY10:15:WD$"prism is parallel to the bottom edge.":15:300:140,70185,14095,140140,70:300:0,1,128::38263fL2:WD$"R O Y G B V":XX270:YY43:5:L45:WD$"Since each color slows by a different amount, each refracts through a different angle.":YY120:15:100:BACK50580gő:WD$"When a prism is used in a spectrometer it is usually set to the refracted angle inside the prism is half of the prism angle A?":YY10:15:300:300:232,96:233,3:29:C13oWƁI110:0:1112,110:5:1112,110::Y110701:0:1112,Y:5 p\ƕ1112,Y:0:1112,Y:5:1112,Y::R016:R:1112,70:R5:1112,first side of the prism.":YY10:15:300:232,93:233,23:1:0nHY89:X701382:X,Y:YY1::1080,102:10135,112:WD$"i":XX90:YY109:5:WD$"r":XX142:YY119:5:126,110128,114126,117nMư100:BACK50600qoRLAST20:150:WD$"Can you see that tw  (0 ѕнй`)JJ & & f)`ɀ` 70:R:1112,70:R5:1112,70:pfƁX112140:16:1X,70:21:1X,70:16:1X,70:21:1X,70::I110:16:1140,70:21:1140,70::pkư100:BACK50600hqpLAST10:150:WD$"If you look closely you can also see that the incident angle is equal to th You won't be able to see them with the telescope. If this happens, rotate the grating by 90 degrees.)":15ztw100:BACK30540z~w2000zPÉ::10:15:"STAND BY....":32767:"RUN SPECTROMETERS P":ye ! Don't touch the surface of the grating itself or allow it to be scratched. (Also make sure it is mounted so that the diffraction pattern is horizontal.":YY10lzjw15:WD$"If it is mounted the wrong way the wavelengths will be dispersed vertically. s the plastic hardens it sometimes shrinks. You may need to use a standard wavelength to experimentally determine d, the distance between slits.":YYYY10:15x[w100:BACK30510x^wy`wWD$"You should be aware of one last thing--the grating is fragil0600rLAST20:150:WD$"Now we can substitute for B....":YY10:15:300:WD$"B":0:XX169:YY40:5:3:WD$"D":YY35:5:WD$"2":YY45:5:168,43175,43:100:BACK50600esLAST20:150:WD$"And we can also replace the refracted angle....":YY10:15:2e refracted angle added to the angle B.":YY10:15:WD$"= + B":XX130:YY40:5:1:0:232,93:233,23qzƔ10110,40:10140,40:WD$"i":XX120:YY45:5:WD$"r":XX150:5:300:300:232,96:233,3:80:I1100:5:176,91:60:176,127::rư100:BACK532,93:233,23:1:0:0:10140,40:WD$"r":XX150:YY45:5:3:WD$"A":XX143:YY35:5:WD$"2":YY45:5sƓ140,43150,43:100:BACK50600MtLAST50:150:WD$"So we have these two relationships:":YY10:15:WD$"=":XX60:YY30:5:1040,30:WD$"i":XX50:Y