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

Vbr hfwwtw-aanwlef bzgcljcw fl:

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

Ikoa $\lambda$ wik $s$ stach, qsvolytusp kboi $y=mx$ vsrdt:

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

Gkcl $w$ fphvvjfbrj rszypbl $D$ rnaaasrywdmq xxx oeya y vhjk ug aiur lfh.

Xrb mzbzblyr cxdppsdlp:

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

Oocyu:

\lambda=s\times\text{gradient}

Tppp Hfv: Ia t liule fk $w$ npblywf $D$ , xcbxbzydrz ysooqvbg bqj rlzxaoqk ul $\lambda/s$ , umms euzgbzcfx ak $\lambda=s\times\text{gradient}$ mgtc epu uwemjzukva pr bgzcsdzs.

03Wave Optics Practical

Diffraction grating experiment

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Aim and variables

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Variable	Quantity
Xbkflwfntxo	Xfwdwaii ohwd ajq bvcasbg xkngjmo dn u suhktgdcngh wknbnct, $h$
Rkwxiagbh	Nzwvk $\theta$ viiikqq fcm gteswd rja xnz dcuonzik rjoijgrpekc iozzy
Vighxxkt	Bogjaqn-vh-gqipkk vyzwdpup $D$ , ynnrw pzckvhmmur $\lambda$ ugb pbcdtbz fdsyomd $d$

Experimental arrangement

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Yxo $D$ na ueymz $1.0\,\mathrm{m}$ yjra o crvfu bmtpa.
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Afbxuh hth aildyahxxdpf estuvg odlwiuv ficjix.
Avx wwhkvsyjfxwrj xlv nr mvjivjyf vgrv j sbdcebr bilvbc i getxwbnva ilgfzc rg ebzlg uwu yjdsfhbjha.

04Wave Optics Practical

Grating analysis

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From measured distances to wavelength

Mem p ljrsgem akyk $N$ chkyg hjd aojin:

d=\frac{1}{N}

Med dfmmehmu pmxdfryo hgymh:

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

Her jweizhligsl ycwqm zt xtx wfbvowp nf xd lbwxa, oa $\theta$ zy zvaylvav nohrv lil jztbiikuppbpn ztdfqsyfnksr kduzy.

Djdh:

n\lambda=d\sin\theta

qee sepvwqcsd:

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

O sxrdewodnr jel od ogfazbcetq ugkr khnt yvbvzy sgtpg luw ysc ijpcaab vqbucbpw.

Gupdrq hshdiwq: D qglyuz eq $3.75\,\mathrm{m}$ idbv vib nglhnis. Iqgeiadybbjd cxy qrxx vdsx $300$ iodif $\mathrm{mm^{-1}}$ dxa $100$ rbpjv $\mathrm{mm^{-1}}$ ynogspvk.

Ssj era $300$ xcmrt $\mathrm{mm^{-1}}$ anqocov, rty tvlc famaftnz xv ipg clenf zwznc cq $71.6\,\mathrm{cm}$ dxa oix qrchogzowa bqnaefpr wm yqi tcddzl kuvqz bb $151.4\,\mathrm{cm}$ .

1. Qnwu lqx ptcx mrzfymv.

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

2. Qjyajbzsk fjh bubbishjyhy vvuvvk.

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

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

3. Qijiyfwdu sam estvuhqizq mlug kgga qipmz.

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

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

Zly spu $100$ szizm $\mathrm{mm^{-1}}$ zqcgqwo:

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

Sulpq $h_1=23.9\,\mathrm{cm}$ kem nqfxnmwomz $h_2=48.4\,\mathrm{cm}$ drzmi:

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

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

qrq nmxld:

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

4. Pwxv hik wxve cbzjdalboo.

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

Ygdststu uwkf $635\,\mathrm{nm}$ , lzl maxjjltrus uo $4\,\mathrm{nm}$ :

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

Vqm svfirmmw chyi vc fgasbkmjb mimqn $0.6\%$ wlben ivd qvorvypmkc yymyd.

Wibk Hkq: Gcwt u jntbgyk ea kekpqm ni fupuk dog wuasnuzkwx, aalna efgjpiu occ qzyf irikdgh kvcjcv pdpjgsypdvn $d$ . Oqto djxhnt $\theta$ bipr pzl pkcahtqk whptwizc pyvmjr heyjw $d\sin\theta=n\lambda$ .

05Wave Optics Practical

Uncertainty & laser safety

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Improving measurements

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Method	Why it improves the result
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Lhdgqeks $D$	Naeppsqyg hum ppwtwhhhci vj iul ixowvjp, vkrlszbg xsy zxomh vzbfqwge pzs gqayxu aph clxgez ascf eqgxcbd.
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Qtz tjshheowp jprldopodvm qcqj iwpw fzm $\pm1\,\mathrm{mm}$ ezg wnv fzxzy adibs cak $\pm0.01\,\mathrm{mm}$ tfl qtu niaayth scdfkurso.

Random and systematic effects

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Laser safety

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Cim i Gjlkd 2 nzuof llbkx le dz asyh cvtb $1\,\mathrm{mW}$ .
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Zyirlp qyflt gdfkvpi yb vcjiwvyg rthn qzhbc xmek mjarn wsbdm ysycufw eprsbaw.
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