optics lab -blackbody radiation - spring 2016

8/18/2019 Optics Lab -Blackbody Radiation - Spring 2016

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Optics Lab

Department of Physics and Astronomy

Blackbody

RadiationSpring 2016

111Equation Chapter 1 Section 11Blackbody

Radiation

Equipment

Included:1 Prism Spectrophotometer Kit OS-8!!1 Optics Bench "#$ cm% OS-8!11 Spectrophotometer &ccessory Kit OS-8'(


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1 &perture Bracket OS-8'!B1 Broad Spectrum )i*ht Sensor PS-+1$1 Rotary ,otion Sensor PS-+1+$1 olta*e Sensor ./-1$$1 Replacement Bulb "1$ pk% SE-8$0

1 Banana Plu* Cord-Black " pack% SE-0(1Required, but not included:1 8$ .niersal /nter2ace ./-$$$1 P&SCO Capstone

Introduction

3his is one o2 the key e4periments that led to the deelopment o2 5uantum,echanics6

3he spectrum o2 an incandescent li*ht bulb is scanned by hand usin* a prismspectrophotometer that measures relatie li*ht intensity as a 2unction o2 an*le6 & Broad Spectrum )i*ht Sensor is used 7ith a prism so the entirespectrum 2rom appro4imately !$$ nm to +$$ nm can be scanned 7ithoutthe oerlappin* orders caused by a *ratin*6 3he 7aelen*ths correspondin*to the an*les are calculated usin* the equations 2or a prismspectrophotometer6 3he relatie li*ht intensity can then be plotted as a2unction o2 7aelen*th as the spectrum is scanned resultin* in thecharacteristic blackbody cure6 3he intensity o2 the li*ht bulb is increasedincreasin* the temperature and the scan is repeated to sho7 ho7 the cures

nest 7ith a shi2t in the peak 7aelen*th6 3he temperature o2 the 9lament o2 the bulb can be estimated indirectly bydeterminin* the resistance o2 the bulb 2rom the measured olta*e andcurrent6 :rom the temperature the theoretical peak 7aelen*th can becalculated and compared to the measured peak 7aelen*th6 3his e4periment should be per2ormed in a room 7ith reduced li*ht leelsalthou*h complete darkness is not required6

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Theory

3he intensity per 7aelen*th /; ";3% as a 2unction o2 7aelen*th o2 radiationemitted by an ideal body "a blackbody since an ideal emitter must also be anideal absorber% is *ien by Planck


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Figure 1: Complete Setup

16 Set up the Prism Spectrophotometer as sho7n in :i*ure 1 e4cept placethe Blackbody )i*ht Source close to the le2t end o2 the track and theCollimatin* Slit closer to it than is sho7n in the picture to ma4imi>e theintensity6 Detailed instructions 2or mountin* the Rotary ,otion Sensorand the De*ree Plate and )i*ht Sensor &rm to the spectroscopy tablemay be 2ound in &ppendi4 '6

+6 &ttach the Broad Spectrum )i*ht Sensor to the )i*ht Sensor &rm usin*the inch bolt "1A! 4 +$% 7ith a lar*e black plastic head6 &ttach the +

inch black rod to the bottom o2 the )i*ht Sensor &rm usin* one o2 theacant holes6 3his makes a conenient handle 2or s7eepin* throu*h thespectrum "see 9*6 1 aboe%6

'6 ,ount the Beeled Stop Piece on the bottom o2 the )i*ht Sensor &rm7ith the t7o supplied bolts "see :i*ure +%6 Position the beeled ed*e soit 7ill hit a*ainst the an*le indicator on the spectroscopy table6

!6 Fote= 3here is a current sensor built intothe 8$ output that is used6 e do notuse the internal olta*e sensor since 7e

7ant the olta*e at the lamp and thereis some drop across the connectin*7ires6

Figure 2: Beveled Stop Piece

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Setup Part B

16 &ttach the ,ounted Prism to the spectroscopy table by scre7in* it intothe hole in the center o2 the table6 Scre7 it do7n until it almost

touches the table6 It is critical that the Mounted Prism does not touchthe tale so the tale is !ree to move "ithout moving the prism# Orientthe prism 7ith its ape4 to7ard the li*ht source as sho7n in :i*ure !6 3he prism base must be perpendicular to the incomin* li*ht beam6 3odo this set turn the table until the inde4 mark is on $o and then setthe base o2 the ,ounted Prism so it lies alon* the $o-18$o line on thetable6 Secure the prism in place usin* the 7in* nut and lock 7asher onthe bottom o2 the bolt stickin* throu*h the spectroscopy table6

+6 Ground the Spectrometer by attachin* an alli*ator ?umper cable 2romthe *round post on the bottom o2 the spectroscopy table "on the side

opposite the Rotary ,otion Sensor% and attachin* the other end to a*round6 & conenient *round is the siler outside connector 2or the H+or H' Outputs at the lo7er ri*ht on the 8$ .niersal /nter2ace6

'6 Plu* the Blackbody )i*ht Source into the H1 Output on the top ri*ht o2the 8$ .niersal /nter2ace6 Polarity does not matter6

!6 Plu* the Broad Spectrum )i*ht Sensor and the Rotary ,otion Sensorinto P&SPOR3 inputs on the 8$ .niersal /nter2ace6 Set the samplerate o2 the )i*ht Sensor to +$ I> and the sample rate o2 the Rotary,otion Sensor to 1$$ I>6

6 Plu* the olta*e Sensor into the &nalo* & input on the 8$ "see :i*ure1%6 &ttach the red lead to the red banana lead on the Blackbody )i*htSource6 &ttach the black lead to the black banana on the Blackbody)i*ht Source6 Do ot attach the leads to the output ?acks on the 8$6 3he current is lar*e enou*h that there is a olta*e drop alon* the 7iresconnectin* the 8$ output to the Blackbody )i*ht Source and 7e 7antto measure the olta*e at the li*ht source6 Set the olta*e Sensorsample rate to +$ I>6


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Figure $: The prism ape% should e oriented to"ard

the light source#

So!t"are Setup

16 Create a *raph o2 Relatie /ntensity s6 &n*le in radians6

+6 Create a table and in the 9rst column create a ne7 .ser-Entered DataSet called J3able &n*le and make the units de*rees6

'6 /n the second column create a ne7 .ser-Entered Data Set calledJSha2t &n*le and make the units radians6

!6 /nsert a third column and create a calculation=

&n*Corr @ L3able &n*le "M% ▼NALSha2t &n*le "rad% ▼Nand make the units de*Arad6

6 Click the Si*nal Generator at the le2t o2 the screen6 Set the 7ae2orm2or DC and the olta*e 2or (6$ either by typin* it in or by usin* theupAdo7n keys to the ri*ht o2 the DC olta*e bar6 Dont turn on thesi*nal *enerator until you are instructed to do so in the procedure "thislen*thens the bulb li2e%6

Procedure

16 Set the collimatin* slits on Slit H!6 Set the &perture Disk in 2ront o2the )i*ht Sensor on Slit H!6

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+6 Collimatin* the system= the Collimatin* Slit must be at the 2ocal pointo2 the 9rst lens and the Sensor ,ask and &perture Disk must be atthe 2ocal point o2 the second lens6 ,oe the spectroscopy table backto the end o2 the track it is out o2 the 7ay6 Place the Blackbody )i*htSource near the end o2 the track and the Collimatin* Slit near theblackbody li*ht source6 ,oe the Collimatin* )ens "see 9*ure 'aboe% at least 1+ cm 2rom the slit6 Iae someone 7ith +$A+$ ision"corrected by *lasses is 9ne% look throu*h the lens at the slit6 ,oethe lens to7ard the slit until it 9rst comes into sharp 2ocus6 3he slitshould be about 1$ cm 2rom the lens6 Fo7 moe the spectroscopytable as close to the Collimatin* )ens as possible6 Set the :ocusin*lens 1$ cm 2rom the Sensor ,ask6 e 7ill ad?ust this more e4actlylater6

'6 Click the Si*nal Generator at the le2t o2 the screen6 3urn on the Si*nalGenerator by clickin* OF6

!6 Set the moeable arm at the center o2 the track so that the un-deiated li*ht that passes aboe the prism 2rom the slit strikes theSensor ,ask6 &d?ust the :ocusin* )ens so the ima*e on the Sensor,ask is as sharp as possible6 3he system isno7 7ell collimated6 )ook at the li*htcomin* 2rom the Blackbody )i*ht Source6Obsere the color6 "es 7hite is a color6%

6 Rotate the moable arm until you see thespectrum6 )ook at the spectrum on the)i*ht Sensor screen6 &re all the colors "2romred to iolet% presentQ hat does this sho7 about 7hite li*htQ

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Figure &: Spectrum on 'ight Sensor Mask

#6 Rotate the scannin* arm until it touches the stop6 3his 7ill be the

startin* position 2or all the scans6

(6 Be2ore startin* to record reie7 the steps you 7ill per2orm durin*recordin*= 3he Broad Spectrum )i*ht Sensor tends to dri2t so the2ollo7in* steps need to be per2ormed as 7ritten6 ith the sensor arepressed a*ainst the stop press the 3are button on the BroadSpectrum )i*ht Sensor "the button is illuminated% to >ero it6 Obserethe "idth o! the visile pattern6 .sin* the handle belo7 the li*htsensor s7eep rapidly 2rom the stop to a position about one visilespectrum "idth to the le2t "ultraiolet side% o2 the pattern6 Slo7lyrotate the scannin* arm throu*h the spectrum to point about t7o

visile spectrum "idths to the ri*ht "in2rared side% o2 the isiblepattern6 ou should try to complete this operation in less than '$seconds 2rom 7hen you press the 3are button but try to s7eep at auni2orm rate6 Fo7 continue rapidly all the 7ay past >ero de*rees "theposition 7here the li*ht sensor is directly opposite the li*ht source%slo7in* as you s7eep across the 7hite li*ht peak at >ero de*rees6 /tis important that you only s7eep in one direction /2 you attempt to*o back the Rotary ,otion sensor 7ill lose track o2 7here you are

86 ou must be holdin* the scannin* arm a*ainst the stop 7hen youpress RECORD /2 it is not a*ainst the stop each run 7ill hae a

dierent >ero position and you 7ill not see the position o2 the peakcorrectly6 Fo7 click RECORD and per2orm the scan as described inpart (6

06 Click Stop6 On the Si*nal Generator click O6 Click on the Si*nalGenerator Button to close the Si*nal Generator panel6

1$6 /2 the cure does not 9ll the *raph click on the Re-si>e 3ool " % at theupper le2t o2 the *raph toolbar6 The angles ma( all e negative)depending on ho" (ou set up the spectrometer# I! so) place the handicon over "here it sa(s *angle+ at the ottom o! the screen and "hen

the lue o% appears) le!t click) select ,uickCalc at the top o! the pop-up and then select ./ in the pop-up that appears to the side# Onboth sides o2 the spectrum peak the Relatie /ntensity should beappro4imately >ero6 /t does not matter i2 the intensity >ero dri2ts asyou s7eep to the central 7hite-li*ht peak as lon* as you can see thepeak6 /2 either o2 these is not true click the Delete )ast Run button atthe lo7er ri*ht and repeat the run6 hen you hae a *ood run clickthe Data Summary button at the le2t ed*e o2 the pa*e double click

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on the *ood run "probably Run H1% and re-label it ( Run6 Click theData Summary button to close the Data Summary panel6

116 E4amine the Relatie /ntensity s6 &n*le *raph6 Fote that it says thatthe unit 2or the an*le is radians6 Since 7e hae only rotated the table

by about 8$o

this is clearly not correct6 3he reason is that the Rotary,otion Sensor measures the an*le that its o7n sha2t turns throu*hbut 7e need the an*le that the table turns throu*h6 3he diameter o2the table is appro4imately #$ times the diameter o2 the Rotary ,otionSensor sha2t6 /t turns out that the number o2 radians 2or the sha2t isappro4imately equal to the number o2 de*rees 2or the table6 emeasure the true correction in step 1+6

1+6 Press the 3&RE button on the Broad Spectrum Sensor6 ith the tableset so the inde4 mark is on $o click RECORD6 Rotate the table 1$$o to the other $o mark let it sit on the $o de*ree mark 2or about ten

seconds "dri2t in the readin* 7ill then make the stop point obious%and click S3OP6 Click Data Summary "top le2t o2 screen% and label thisrun Calibrate6 Close the Data Summary panel6 On the *raph selectthe Calibrate Run6 :ind the an*le "rad% that the sha2t turned throu*h6 3he initial an*le should be e4actly $6 3o 9nd the 9nal an*le click on

the Data Selection icon " % on the *raph toolbar6 & hi*hli*htedre*ion 7ith handles should appear on the *raph6 Dra* the handles tohi*hli*ht the re*ion bet7een 1$$o and 1$#o6 Click the Scale-to-:it tool

" %6 ou should no7 be able to read the an*le to the nearest tentho2 a de*ree6 Record this alue in the table in the Sha2t &n*le column6

our alue should be close the one already in the table but chan*ethe alue to the one you measured since the instruments may arysli*htly6

1'6 Click on the Calculator on the le2t side o2 the screen and create acalculation=

true angle0#&34as56angle 5rad7)▼ 87 and give it units o! o 5degrees7#

I! (our value di9ers !rom the sample data) replace the sample value 5#&37

"ith (ours in the calculation !or the true angle# "1$$oAsha2t an*le @ $60#0%On the *raph delete the selection and then click on the Scale-to-:it tool to

return the *raph to normal6

1!6 Create a ne7 pa*e and create t7o di*its displays 7ith the olta*eCh6& and Output Current and create a *raph o2 Relatie /ntensity s6true an*le6 3here 7ill be a peak on the intensity s6 an*le *raph7here the li*ht sensor is ali*ned 7ith the li*ht source because someli*ht passes by the prism instead o2 *oin* throu*h the prism6 3hispeak enables the initial an*le to be e4actly determined6 Select the (

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Run i2 it isnt already displayed6 Click the Scale-to-:it tool6 Click on the

Coordinates 3ool " % 2rom the *raph toolbar6 Click on the bo4 anddra* it until it is directly aboe the central peak "aboe it not on theline T you should see an arro7 pointin* do7n to the peak6 Release theSmart Cursor and it 7ill snap to the peak6 3he t7o numbers in the

in2o bo4 are Lan*le relatie intensityN6 Click the Calculator "le2t side o2 screen% and enter this equation=

CorrTrueAng= Initial Angle−True Angle

and de9ne /nitial &n*le to be the an*le read on the *raph6 3his amount 7illbe subtracted 2rom all the an*les so 7e are measurin* the an*le that theli*ht bent 2rom the strai*ht throu*h path6

16 Repeat Steps # throu*h 0 2or olta*es o2 ! and 1$ 6 #aution: /2 1$olts is applied to the blackbody li*ht 2or an e4tended amount o2

time the li2e o2 the bulb 7ill be reduced6 Only turn on the bulb 7hentakin* measurements6 Fotice "7ith your eyes% ho7 the spectrumchan*es6 On a ne7 pa*e in Capstone create a *raph o2 )i*ht/ntensity s6 3rue &n*le and select the ! Run6 .se the Smart Cursorto eri2y that the central peak a*rees 7ith the ( Run 7ithin $61de*rees6 3hen check the 1$ Run6 I! the central peaks disagree (more than #1 degrees) (ou did not start !rom the same position5against the stop7 and should redo one or more runs#

Analy$i$ Part 1

3he 7aelen*ths ";% 2or the 3un*sten Cures are calculated 2rom themeasured dispersion an*les6 See &ppendi4 1 "&UB% 2or details o2 thiscalculation6 3he lar*er the an*le the shorter the 7aelen*th6 3he7aelen*ths are limited to the ran*e !$$ nm to +$$ nm since therelationship relatin* an*le to 7aelen*th is only alid 2or this ran*e andbecause the *lass o2 the prism does not pass 7aelen*ths aboe +$$ nm6

/n the calculator create the 2ollo7in* equations "see &ppendi4 ' 2ore4planations o2 these equations%=

%cal&'()*1+-Inde. o! Re!raction/012'34*)(+-Inde. o! Re!raction/0

12'345(*)16+-Inde. o! Re!raction/012'345'

n&$qrt(7$in-#orrTrueAn8 94/4+$qrt'4*)345(*'+4

λ=filter (400,2500, λcal)

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On a ne7 pa*e in Capstone create a *raph o2 )i*ht /ntensity s6 aelen*th;6

/2 the ! ( and 1$ cures dont all sho7 on the *raph click the Data

Selection 3ool " % so that it is pushed in and then click the small black

trian*le and select all three runs6

16 Does the peak shi2t to7ard shorter or lon*er 7aelen*ths as thetemperature is increasedQ

+6 Io7 does the intensity chan*e as the temperature is increasedQ Doesthis a*ree 7ith 7hat Equation + "see 3heory% predictsQ

'6 Io7 did the color o2 the bulb chan*e 7ith temperatureQ Io7 did thecolor composition o2 the spectrum chan*e 7ith temperatureQ Considerin* thepeak 7aelen*ths 7hy is a bulbs 9lament red at lo7 temperatures and7hite at hi*h temperaturesQ

!6 &t about 7hat 7aelen*th is the peak 7aelen*th o2 our SunQ hatcolor is our SunQ hyQ

6 :or the hi*hest temperature is more o2 the intensity "area o2 theintensity s6 7aelen*th *raph% in the isible part o2 the spectrum or in thein2rared part o2 the spectrumQ Io7 could a li*ht bulb be made more eVcientso it puts out a *reater percenta*e o2 its li*ht in the isibleQ

Temperature16 On a ne7 pa*e create a table 7ith a ne7 .ser-Entered Data set called

JR holder 7ith units o2 W in the 2irst column6 3hen create the 2ollo7in*equations in the calculator=

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'6 Put in the alues 16$ W6 +6$ W and !6$ W 2or the resistance o2 the )ampIolder "Rholder% in the 9rst column o2 the table6 3hese alues are *iento sho7 ho7 sensitie the 3emperature alue is to this measurement6

!6 Create a *raph o2 )i*ht /ntensity s6 7aelen*th ;6 Click on the DataDisplay icon " % on the *raph toolbar and select the ! Run6 Click

the Re-si>e 3ool " %6 .se the Smart 3ool " % on the 3un*sten/ntensity s6 aelen*th *raph to 9nd the 7aelen*th 7here theintensity is ma4imum6 /t is probably best to ?ust eyeball the center o2the peak rather than usin* the Snap to the peak 2unction o2 the SmartCursor 7hich tends to be con2used by the rather Xat peak6 Calculatethe temperature usin* Equation "+% 2rom the 3heory section6 Repeat 2orthe ( Run and the 1$ Run6

Analy$i$ (: Planck@$ Equation

16 Calculated temperatures "2rom ma4 7aelen*th% =a6 1$ Run=b6 ( Run=c6 ! Run=

+6 Does your calculated temperature a*ree 7ith that in2erred 2rom the9lament resistanceQ

'6 Create the 2ollo7in* calculations "e4plained in &ppendi4 '%=

I&-#1/+-% nm4/+1)564534 1+e.p-#(/+-% nm4/+1)5647-Temp/401444

Itheory&-I/7171)5011447-$cale/

#1&(77-Planck$ con$tant C$4/7-Speed o! li8ht m+$4/5(

#(&-Planck$ con$tant C$4/7-Speed o! li8ht m+$4/+-Boltmann$con$tant C+F4/

Temp&(3))

$cale & 1)(

!6 On the *raph o2 )i*ht /ntensity s6 7aelen*th create a second erticala4is and select the theoretical /ntensity "/theory%6 Click on the Data

Display icon " % and select the 1$ Run6 Click the Re-si>e tool "

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%6 Chan*e the temperature "3emp% in the calculator to match yourcalculated temperature aboe6 Be sure that the scales on the le2t andri*ht sides o2 the *raph are the same /2 they are not chan*e one o2the scales by moin* the cursor aboe a number on that ertical scaleand 7hen the hand icon chan*es to a parallel plate icon click and dra*

to stretch the scale until both are the same6

6 3he Jscale is included in the calculation because the Broad SpectrumSensor is not calibrated6 &lso 7e need a scale 2actor o2 rou*hly 1$-11 that is built into line 11 in the Calculator to ad?ust 2or the 2act that thereadin* 2rom the li*ht sensor is in units o2 Y but the units o2 the theoryare in Am'6 3he Jscale is currently 16$+6 Chan*e this until theBlackbody cure "/meas% rou*hly matches the 3un*sten cure but isaboe it eery7here6

#6 Does the shape o2 the cure match the theoretical cureQ Can the bulb

really be considered a blackbodyQ

(6 Real ob?ects radiate less than a Blackbody6 :or a real ob?ect /real @e" ;%/Plank 7here e" ;% is called the emissiity and is a 2unction o27aelen*th and is al7ays less than 16 :or uno4idi>ed tun*sten at +$$$K the alue o2 e" ;% aera*ed oer all 7aelen*th is $6+#$ and at '$$$K it is $6''! "CRC Iandbook #'rd edition pa*e E-'8(%6 3o sho7 thetrue blackbody cure triple the Jscale alue so the Blackbody cureis about '4 as hi*h as the 3un*sten cure6 ou 7ill need to ad?ust theertical scales6 :irst ad?ust the /theory scale on ri*ht until the /theory plot allsho7s on the *raph6 3hen ad?ust the le2t hand scale until both scales

are the same6 3un*sten actually peaks at a 7aelen*th about +$ nmshorter than the Blackbody peak6 3his is too small to see in your data6 ou no7 hae the true and ideal cures 2or tun*sten6

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Z

Z+Z'

Appendi. 1= :indin* the 7aelen*th as a 2unction o2 an*le6

aelen*th Calculation= 3he inde4 o2 re2raction o2 the prism *lass aries 7iththe 7aelen*th o2 the li*ht6 3o determine the 7aelen*th as a 2unction o2 thean*le the relationship bet7een the inde4 o2 re2raction and the an*le isdetermined usin* Snells )a7 at each 2ace o2 the prism and some *eometryand basic tri*onometry6

sin #$o @ n sin Z+ "&1%and sin Z @ n sin Z' "&+%

7here n is the inde4 o2 re2raction o2 the prism6

n sin Z' @ n sin "#$o - Z+% @ n"sin #$o cos Z+ - cos #$o sin Z+%

@ n sin #$o cos Z+ - cos #$o sin #$o "usin* Equation &1%

Rearran*in* this and usin* Equation &+ yields

n cos Z+ @ "sin ZAsin #$o% [ sin #$o "&'%

Squarin* Equations &1 and &' and addin* them to *ies

n+ "sin+ Z+ [ cos+ Z+% @ n+ @ L"sin ZAsin #$o% [ sin #$oN+ [ sin+ #$o

Puttin* in alues 2or sin #$o and cos #$o yields

n=

√( 2

√ 3sinθ+ 1

2 )2

+ 34 "&!%

e use this equation to calculate inde4 o2 re2raction "n% alues 2or ourmeasured an*les6 e then use the n alues to calculate the 7aelen*thusin* alues relatin* the inde4 o2 re2raction to 7aelen*th 2or the prism"proided by the supplier o2 the prism%"see table under tab &ppend 1B%6

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e need an equation based on the data in the table to use in ourcalculations6 e use a polynomial and choose the alues o2 the constants to9t the prism data6 3he results are not unique but 9t the data 7ithin theuncertainty in the inde4 implicit in the data table o2 at least $6$$6 3he

equation is ; @ & [ B"n-E%-1 [ C"n-E%-+ [ D"n-E%-' "&%

7here ; is the 7aelen*th in nm and the constants hae alues= & @ '+$nm B @ 1 nm C @ $6+ nm D @ $610 nm and E @ 16#'6 On the *raph theopen circles represent the prism suppliers data 7ith the si>e o2 the circlessho7in* the uncertainty and the cured line is 2rom the aboe equation6

1

/nde4 o2 Re2raction aelen*th " nm %

16#8 +'+6!$16#0 10($61$16#0 1+06#$16($ 1$#$6$$16($ 1$1!6$$16(1 8+61$16(+ ($#6$16(+ ##6'$16(+ #!'6$$16(+ #'+68$

16(' 806'$16(' !#61$16( !8#61$16(# !'68$16(8 !$!6($


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Appendi. ( Gindin8 the Temperature

3he resistiity o2 3un*sten oer a broad ran*e o2 temperature is sho7n in thetable "CRC Iandbook #'rd edition pa*e E-'8(%6 & 2unction that appro4imatesthe data is also *ien

3"K% @ 1$' [ '861\ T $6$0\+

[ $6$$$+!8\'

"%

7here \ is the resistiity in units o2 1$-8 W-m6 3he *raph sho7s the 2itbet7een the measured alues o2 3"K% 2rom the table "circles% and the alues2rom equation "line%6

6

1#

resistiity"H1$-8W]m%

3emperature"K%

resistiity"H1$-8W]m%

3emperature"K%

6# '$$ #$6$# +1$$86$# !$$ #'6!8 ++$$

1$6# $$ ##601 +'$$1'6+' #$$ ($6'0 +!$$1#6$0 ($$ ('601 +$$106$$ 8$$ ((6!0 +#$$+160! 0$$ 816$! +($$+!60' 1$$$ 8!6($ +8$$+(60! 11$$ 886'' +0$$'$608 1+$$ 0+6$! '$$$'!6$8 1'$$ 06(# '1$$'(610 1!$$ 006! '+$$

!$6'# 1$$ 1$'6' ''$$!'6 1#$$ 1$(6+ '!$$!#6(8 1($$ 11161 '$$$6$ 18$$ 116$ '#$$'6' 10$$ 116$ '#$$#6#( +$$$ 116$ '#$$


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e may i*nore the e4pansion o2 the 9lament to *ood appro4imation so theresistiity is directly proportional to the resistance and 7e 7rite

\A\o @ R9lARo @ "Rmeas TRholder%ARo @ "A/ T Rholder%ARo

\ @ \o"A/ T Rholder%ARo "&(%

7here \o is the resistiity at room temperature "\o @ 6#41$-8W-m% Ro is theresistance o2 the 9lament at room temperature "Ro @ $60' W% R9l is theresistance o2 the 9lament at some temperature Rholder is the resistance o2 thelamp holder Rmeas @ A/ is the measured resistance o2 the bulb holder [lamp / is the current throu*h the 9lament and is the olta*e measureddirectly across the lamp holder6 By measurin* / and Rholder and usin*Equations U &( 7e determine the temperature o2 the 9lament6

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Appendi. ': E4planation o2 Equations in Capstone :ile

Fote that the do7n arro7 "▼% indicates that you can click on it to choose aspeci9c run o2 that measurement rather than hain* the calculation apply toall runs6 Formally calculations are 2or all runs e4cept 7hen you may 7ant to

subtract a particular run 2rom all the other runs as you may do 2orcalibration6

16 &n*Corr@L3able &n*le "M% ▼NALSha2t &n*le "rad% ▼N

AngCorr=Table Angle(degrees)

Shaft Angle (rad)

3his equation ad?usts 2or the 2act that as the sha2t o2 the Rotary ,otionSensor rotates throu*h one reolution the table only rotates throu*h 1A#$th

o2 one reolution6

+6 ;cal@'+$[1A"L/nde4 o2 Re2raction ▼N-16#'%[$6+A"L/nde4 o2 Re2raction▼N-16#'%^+[$610A"L/nde4 o2 Re2raction ▼N-16#'%^'

λcal=320+ 1

(n−1.635)+

0.2

(n−1.635)2+

0.19

(n−1.635)3

3his equation uses the in2ormation 2rom the manu2acturer o2 the prism todetermine the 7aelen*th as it depends on the inde4 o2 re2raction6 3he

numbers are *ien to us by the manu2acturer6 3he manu2acturer determinesthese numbers empirically6

'6 3cal@1$'['861L\ "1$_` W-m% ▼N-$6$0L\ "1$_` W-m%▼N^+[$6$$$+!8L\ "1$_` W-m% ▼N^'

T cal=103+38.1 ρ−0.095 ρ2+0.000248 ρ3

3his equation calculates the temperature o2 the 9lament 2rom the resistiity7hich is determined by the olta*e across the 9lament and the current

throu*h the 9lament6 3he equation comes 2rom the CRC Iandbook relatin*ho7 the resistiity o2 3un*sten chan*es 7ith temperature6

!6 true an*le@$60#0abs"Lan*le "rad% ▼N%

trueangle=0.9569|(angle)|

18


19/24

3he true an*le is calibrated by moin* the spectrometer arm throu*h akno7n an*le read 2rom the spectrometer table and readin* the an*le 2romthe Rotary ,otion Sensor6 3he number is entered by the user and iscalculated by takin* the ratio o2 the 3able &n*le in de*rees oer the Rotary,otion Sensor &n*le in radians6 3here2ore the true an*le is in de*rees6 3he

absolute alue o2 the Rotary ,otion Sensor is taken to ensure a positiean*le een i2 the Rotary ,otion Sensor happens to be set up so that it readsne*atie6

6 Corr3rue&n*@L/nitial an*leN-Ltrue an*le ▼N

CorrTrueAng= Initial Angle−True Angle

3he Corr3rue&n* is measured 2rom the central ma4imum6 3he /nitial&n*le is the an*le o2 the central ma4imum measured on an /ntensity s6 3rue&n*le *raph6

#6 n@sqrt""+sin"LCorr3rue&n* "M% ▼N%Asqrt"'%[$6%^+['A!%

n=√( 2sin (CorrTrueAng)√ 3 +0.5)2

+3

4

3his equation is deried in &ppendi4 16 3he inde4 o2 re2raction n o2 theprism *lass aries 7ith the 7aelen*th o2 the li*ht6 3o determine the7aelen*th that corresponds to the an*le the li*ht is bent the inde4 o2re2raction must be kno7n6

(6 ;@9lter"!$$+$$'+$[1A"Ln ▼N-16#'%[$6+A"Ln ▼N-16#'%^+[$610A"Ln▼N-16#'%^'%

λ=filter (400,2500, λcal)

3he 7aelen*th ;cal determined 2rom the an*le is *ien by Equation "&% in&ppendi4 16 /t is 2ound 2rom the alues *ien by the prism manu2acturer6 3hisequation is a 9lter that only *ies a alue 2or the 7aelen*th i2 the7aelen*th is bet7een !$$ nm and +$$ nm 7hich is the use2ul ran*e o2

the prism *lass6

86 resist@6#"Lolta*e Ch & "% ▼NALOutput Current Ch I "&% ▼N-LRholder "ohm% ▼N%A$60'

:rom &ppendi4 + the equation 2or the resistiity is=\ @ \o"A/ T Rholder%ARo

10


20/24

7here \o is the resistiity at room temperature "\o @ 6#41$-8W-m% Ro is the

resistance o2 the 9lament at room temperature "Ro @ $60' W%

ρ=5.65 ( V

I − Rholder

0.93 )06 &bs 3emp@1$'['861Lresist "1$_` W-m% ▼N-$6$0Lresist "1$_` W-m%

▼N^+[$6$$$+!8Lresist "1$_` W-m% ▼N^'

|Temp|=103+38.1 ρ−0.095 ρ2+0.000248 ρ3

1$6 /@"LC1NA"L; "nm% ▼NA1$^0%^% "1A"e4p"LC+NA""L; "nm%▼NA1$^0%L3empN%-1%%%

I =C 1 λ

5 ( 1

e

C 2

λT −1 ) 3his is the theoretical equation 2rom the theory Equation "1%6 3hetemperature is entered by the user in the constant equation belo7 "1!% toaect the shape o2 the cure6

116 /theory@L/ ▼N"11$^"-11%%LscaleN

I theory=( I 10

−11

)(scale)

3his is the theoretical equation multiplied by a 2actor o2 1$-11 to makethe alues in the same ran*e as the measured li*ht intensity alues that arein percent o2 ma4imum6 /t is also multiplied a scale 2actor that you can ad?ustto make the hei*ht o2 the theoretical cure match more closely to the data6 3his calculation does not aect the shape o2 the cure6

1+6 C1@+LPlanck


21/24

1!6 3emp@+$$

16 /nitial an*le@#860

1#6 scale @ 16$+

+1


22/24

Appendi.

Spectrophotometer Set p

3his part o2 the manual describes ho7 to set up the Spectrophotometer System "see :i*6 '%6

Jountin8 the Rotary Jotion Sen$or 3his describes ho7 to mount the Rotary ,otion Sensor to the hin*e on theSpectrophotometer Base6 3he top o2 the Spectrophotometer Base has a short threaded post2or centerin* the circular De*ree Plate and 2or holdin* the Gratin* ,ount6 /t also has ama*netic pad 2or holdin* the De*ree Plate and a trian*ular shaped inde4 marker6 One sideo2 the base has a post upon 7hich the Pinion can be stored 7hen it is not in use6 3he otherside has a sprin*-loaded hin*e and t7o small thumbscre7s 2or mountin* the Rotary ,otionSensor "included in the Spectrophotometer System%6 On both sides o2 the base are lar*e

++


23/24

thumbscre7s and square nuts used 2or mountin* the Spectrophotometer Base on the OpticsBench "see :i*6 !%6

3he Rotary ,otion Sensor has a three step pulley attached to its sha2t 7ith a smallthumbscre76 3he sensor also has a rod clamp attached at one end6 :irst remoe the smallthumbscre7 and three step pulley 2rom the Rotary ,otion Sensor sha2t6 3hen remoe therod clamp 2rom the Rotary ,otion Sensor "see :i*6 %6 Remoe the t7o small thumbscre7s2rom the threaded stora*e holes on the side o2 the Spectrophotometer Base and set them

aside 2or the moment6 Remoe the Pinion 2rom the stora*e post on the opposite side o2 theSpectrophotometer Base and set the Pinion aside 2or a moment "see :i*6 #%6 Rotate the hin*ea7ay 2rom the side o2 the base until the hin*e is almost perpendicular to the base6 .se thet7o small thumbscre7s to 2asten the Rotary ,otion Sensor to the lo"er set o2 holes on theinside o2 the hin*e6 Place the Pinion all the 7ay onto the Rotary ,otion Sensor sha2t andti*hten the Pinion on the sha2t by turnin* the small thumbscre7 on the side o2 the Pinion"see :i*6 (%6 Connect the Rotary ,otion Sensor to the P&SCO inter2ace6

+'


24/24

Jountin8 the De8ree Plate and Ki8ht Sen$or Arm 3he De*ree Plate and )i*ht Sensor &rm are shipped as a unit6 3he )i*ht Sensor &rm isattached to the circular De*ree Plate 7ith t7o small thumbscre7s6 3he hole in the center o2the De*ree Plate 9ts oer the short threaded post on the top o2 the SpectrophotometerBase6 Iold the Rotary ,otion Sensor sli*htly a7ay 2rom the base so the small diameter poston top o2 the Pinion is not in the 7ay o2 the ed*e o2 the De*ree Plate6 Position the hole in theplate oer the short threaded post on the top o2 the base6 Place the De*ree Plate onto the

Spectrophotometer Base6 )et the small diameter post on the top o2 the Pinion rest a*ainstthe edge o2 the De*ree Plate "see :i*6 8%6

+!

optics lab -blackbody radiation - spring 2016

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