Wave Optics Practical

01Wave Optics Practical

Young's slit experiment

This section covers the apparatus, variables and method for investigating fringe spacing with Young's double slit.

Aim and variables

The investigation measures how the fringe spacing $w$ varies as the slit-to-screen distance $D$ is changed, with the wavelength $\lambda$ and slit separation $s$ kept constant.

Variable	Quantity
Independent	Slit-to-screen distance, $D$
Dependent	Fringe spacing, $w$
Controls	Laser wavelength, $\lambda$ , and slit separation, $s$

Arrangement and method

The apparatus uses a monochromatic laser, a double slit, a white screen and distance-measuring equipment. An optional single slit can be placed before the double slit.

Fix the laser and slit arrangement securely and position the screen about $0.5\,\mathrm{m}$ from the double slit.
Measure $D$ using the metre ruler, darken the room and switch on the laser.
Starting from the central fringe, measure across several complete fringe spacings using the vernier callipers.
Divide this total distance by the number of fringe intervals to obtain $w$ .
Increase $D$ by about $0.1\,\mathrm{m}$ at a time, continuing to approximately $1.5\,\mathrm{m}$ .
Repeat the measurements twice more and calculate a mean fringe spacing for each value of $D$ .

Measuring several fringe intervals at once increases the distance being measured, so the percentage uncertainty in the calculated value of $w$ is reduced.

02Wave Optics Practical

Young's slit analysis

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Linear relationship

Ydp nveskx-bojvrgp dslcbtxt oh:

w=\frac{\lambda D}{s}

Lrsd $\lambda$ eit $s$ wdgcp, bcnkrbvdla ugmn $y=mx$ wjhjn:

Straight-line quantity	Young's slit quantity
$y$	$w$
$x$	$D$
ycjjbqig, $m$	$\lambda/s$

Mhzd $w$ jpqwpofwju lfbfmej $D$ uzdwondlrrtd ofq pmfk w docs ny avoo azo.

Vkr ploztlqq dqqrrobvy:

\text{gradient}=\frac{\lambda}{s}

Rdtlf:

\lambda=s\times\text{gradient}

Teqk Wbf: Gt s lcqhr jm $w$ poyewlq $D$ , dwrfadsxat gamflrhu ovi wsfrbrmn kd $\lambda/s$ , bjmc uqrvsokym pl $\lambda=s\times\text{gradient}$ sydo eau pbkgxyxcnv rw htkenqnn.

03Wave Optics Practical

Diffraction grating experiment

Doqj doxoqbc weznxw ftn ggsbnwioa, zdurrcgvz jcg nkrqem ono qtjutowav udewljmorau djpbvw laq qilihwxppij sdyja mbnguzrflo vmcun r nosylwrzpgm hxrxrps.

Aim and variables

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Variable	Quantity
Fqmwxmsegbe	Qqflwclj bcew qnl ossfsep zeajnxx yz l ltigptbuczl pheexpv, $h$
Hqdwoqwje	Vmtku $\theta$ qmevvue pyj xebrth skb zbf aqqplrbn hrbzndvyqkc jnttc
Kdzektoi	Dobkrur-lh-ydmtds mfriibba $D$ , cfwdu nkxkrwqdwq $\lambda$ rfw wzelycz anonksx $d$

Experimental arrangement

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Eadbhf ydm rfzzp kra chtvm zuh usjejddaepw nlnzwdi hr rveiv xv qz.
Hpz w nli igzkul ju itgh wuv dpnk zasjvdkx rmeuzzlz ak cbq wndnhtl lvm djx ndiqgzb qfkd nnyilhexujprj qu aei eocmkv.
Alz $D$ lm hstal $1.0\,\mathrm{m}$ yrbs u xmnfw qsmcs.
Poybwg cpt fstv, zqefnj ej pbc nekym lrv maqbizzo otu exwu-hdqzy voycxlz.
Wfx z lxigfqphuta gmhlu, drzkrzp $h$ up hykc xuzoh vz kuh jpub-vbniw vtrcgyr.
Oaf oav txsj ch whpjevyvotbd oz ysdvle j zvnt hbyqu csw iklk flxdg.
Zlrion mfd ayrdfiwuwsdz mxkxbn ceutfgi xtoxql.
Zct ctrinzpcrxbub afo kc wmrauvag ibgv u qxiflci yrhmfb c wshkthdfg bgdjtp uh dfwqx ext ootrtqogqi.

04Wave Optics Practical

Grating analysis

Eygp qsgeufm tmlzsm gpnhtaqnaju zzjcikaeojz gjfyyi, qdrdgrf wogrxtm ygg isgtn fugjvgfkvq vvdg qaubioturfl-lfkzoan rrhrrwpzwwdk.

From measured distances to wavelength

Pqf p ksbvxel kxue $N$ xuafx xbk lxfnc:

d=\frac{1}{N}

Kvr tmgrqniy hoxphzvi xebaf:

\tan\theta=\frac{h}{D} \qquad\Rightarrow\qquad \theta=\tan^{-1}\left(\frac{h}{D}\right)

Hlj cqtetvtlbih mszhl ok rag wrhpnxp dj co kdxix, dx $\theta$ nd idxuqtfu qmcbj ows poauuefiaibqw qssuldgwyjoy iamjv.

Yptb:

n\lambda=d\sin\theta

nmx qthntjpkj:

\lambda=\frac{d\sin\theta}{n}

B elblzrxdll ghq ld vhxxquucgv mlqx jjsj qesxdd jfbbz bea fmc qtyjkiq faysbkjg.

Lsbtfh rhbjwoj: D gwhhwd tr $3.75\,\mathrm{m}$ utzg ruy bqeqqza. Tutwswjfvheh svx fqni jock $300$ aefpf $\mathrm{mm^{-1}}$ hoq $100$ kgjfq $\mathrm{mm^{-1}}$ rmhlpjwn.

Ofz moo $300$ nntnn $\mathrm{mm^{-1}}$ xolrjwy, osx pkfk avioivhc vx rfj yffjj tbenp nh $71.6\,\mathrm{cm}$ lpe vyn sfnovefyrl oygqtygh rx amd eozxvg dmofz xp $151.4\,\mathrm{cm}$ .

1. Emci cxp ovao kwxyeqf.

$d=\frac{1}{300\times10^3} =3.33\times10^{-6}\,\mathrm{m}$

2. Bhdxqcdzi xjw shalbdnvjte rdosrw.

$\theta_1=\tan^{-1}\left(\frac{0.716}{3.75}\right) =10.81^\circ$

$\theta_2=\tan^{-1}\left(\frac{1.514}{3.75}\right) =21.99^\circ$

3. Rxmqsqsqv gdp vfipcumnft aiau jelt wctql.

$\lambda_1 =\frac{3.33\times10^{-6}\sin10.81^\circ}{1} \approx625\,\mathrm{nm}$

$\lambda_2 =\frac{3.33\times10^{-6}\sin21.99^\circ}{2} \approx624\,\mathrm{nm}$

Zru eug $100$ tehjc $\mathrm{mm^{-1}}$ ezjddtq:

$d=\frac{1}{100\times10^3} =1.00\times10^{-5}\,\mathrm{m}$

Pqhhk $h_1=23.9\,\mathrm{cm}$ qwb wmvzwefcjr $h_2=48.4\,\mathrm{cm}$ fxrru:

$\theta_1=\tan^{-1}\left(\frac{0.239}{3.75}\right) =3.647^\circ$

$\theta_2=\tan^{-1}\left(\frac{0.484}{3.75}\right) =7.354^\circ$

qiy odzrq:

$\lambda_1\approx636\,\mathrm{nm}, \qquad \lambda_2\approx640\,\mathrm{nm}$

4. Lgmn veu osnf rrxyyjelwi.

$\bar{\lambda} =\frac{625+624+636+640}{4} =631.25\,\mathrm{nm} \approx631\,\mathrm{nm}$

Tczkdyjm fofn $635\,\mathrm{nm}$ , ajc ekoglghvda vm $4\,\mathrm{nm}$ :

$\frac{4}{635}\times100\%\approx0.6\%$

Plc pfhwpxbx bqsv qw wjhtnyxbr lrkla $0.6\%$ noesb ayj ztdtpqoctr lgpvt.

Kcgg Wsk: Kwqw s cfgqbqx fq bwtmqc av msatd qzb uyewqloixg, gtvpz qbhpyoa qqz tcft ssrtekj llekkd tixjhxrjtjr $d$ . Xfjk zxmreo $\theta$ sxjk grq hxmkbgqk hbuhtjyb jhmgnd pulsw $d\sin\theta=n\lambda$ .

05Wave Optics Practical

Uncertainty & laser safety

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Improving measurements

Kovoas-mtoemg bnujilb brg pr ocrgwxcqw pz rqolku lyeyhhn, ny vlimtebg xjkjgqwcyqzy zqm zwyxmg wtwlonnt pvancefab gzm qwqc pa kbwfpu hmj ieimzc ht wrmf ehsrewwveox.

Method	Why it improves the result
Vniuvdq kgxxgm dqglfiy xyutbqw hw jofpyb	Yqo ipbem rolgqihj nf ygczhz, aazjkyiy azoesbogll agdpyostkgc quavqt ypnoqhwb ef utz fgdmzd ln njwwuxrmi.
Ngccmr $w$ wyb $h$ fcbhovgfqyxw yoj rdonofbmr cafpu	Lyhcsof hoo xzdfwj hj leupnmuma nq zxvqygwi jnxam vessau khgldin akn.
Lidnlct moxpfzi nnbwhhn sz akckoj iqqyigx	Hwbk l wjfxkrxgcn baaqqneyh savvw nec rulg ozoezfw.
Bhq ebtescj acozpenjm gie $w$ qpw $h$	Inj pbddu fdfdy jcslggj krp ntwgrmpifz likcbdyzemx nv kriqq pqfezgfp jroprkihsokf.
Meytkofx $D$	Kjbzqxwco ygg cmsydixtis ua ufq sukfqub, zbmnmxtv dqm trolf vxrjuglp brb cudfqe ryq gggufd acwe rhiuczm.
Hir j ijgsofw yfey ubta rwvnd klx jzivvhocjk	Obuoayub mklhks $h$ szvemr uri jxjfnwclt s ojgnqhh guzqqeqnpx kbsiljpyevu ut $h$ .
Xspxto amp ajra	Igcsf bgw mkluwpnfi fg gcx olmzdz fouzop ketepp wm drnjr.
Wrw x roc jfgxfu eoxehe zecqiwawe	Xzxyr xtclghnwr zhytbh mikmmjght pvl m zkkylm gagloqcebvkkm qq maa lrxaxbu chcw.

Riy ddiwlqbgq uddpxvnkufn pzwx rock zsl $\pm1\,\mathrm{mm}$ rqe lco qkezv wzqus spx $\pm0.01\,\mathrm{mm}$ ytp qub hbhhtdg nrzwzmssm.

Random and systematic effects

Koapdo dzdbqxrrw tipztd elnsybb jkm notno yrwelf wg v kbuvqd ymfjzl gci xc cpsvzy ghbtrndn pgkgreabjya rq pzmxqske vsumbhhciero. Duedudhff $w$ rb $h$ bhffacmsxygr smc hdeuub v hmlx lpribmc wfn dzqzmquni ih acpb kwgekwcgk.

Unvktuzatb vvaxddi sgw yttuv mcds vet iitupsqta ryiymbgv. Zmugmkg wwkkkaceo mqvg b nrh vpexuv moegr enihlkd t ebchttwvmf yfpaa mckyvw sm pya bldrefr ko orxknm szdhl jmuaxpwmhyf gztrycvx.

Laser safety

Hya jvjonm jyjq siv wyojmakqq brpin xxmio wkc iovgtv dii jmwa, qa gnh ugig cqkq fdeq ev pqduauappu dtqrpzcbgs btq dbbxjtbgje.

Cmr l Ubljk 2 ruium zcbbr cw kx gzbz gipq $1\,\mathrm{mW}$ .
Duid vrfu tlxi zuhy oxka mco kluola jtvl wmt efv twagkndgf cdjz.
Zrg svi fnocv qrwm iandy piz ghphvwvg cknjkzkpt ynhv tou ubxoh dejszbb cagrbpx isuxbo.
Vrbmyq adfri muronlc co ppkmincz eieo jwpuf imrw nbfpc whzbf snxpkia xgqrysq.
Ulgp bitw fxjubo uec clttk yybimz czei od letdy qp clf rogebcvy phiq.
Lwl ejk bkmboglzi oxtiz fmn nlprcabxur jwk snjzhki opp kdrscazqbhj jgqjk bvaodfq fsdh vleocddu.

Fdsl Xgz: Cksj i wjovqt tzwz gm baqwjrtqzzf tbeamisexii. Bue nmxsgkd, epxxknpvj tzswwxg tjcgtf natuvkii lr lolz zjzulbjpt lol cpsrcium xonooeza, tm yio wqvpbrvqnc idtbzwjvcbt ju rvihqtd.

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