Refraction & TIR

01Refraction & TIR

Refraction

This section covers how light changes direction, speed and wavelength when it crosses a boundary between media.

Refraction at a boundary

Refraction is a change in the direction of a wave at a boundary when its speed changes. In optics, the media on either side of the boundary are transparent materials.

The amount of bending depends on the optical properties of the two media. Light entering a medium with a higher refractive index slows and bends towards the normal. Light entering a medium with a lower refractive index speeds up and bends away from the normal.

Into a higher- $n$ medium

Wave speed decreases.
Wavelength decreases.
Frequency stays constant.
The ray bends towards the normal.

Into a lower- $n$ medium

Wave speed increases.
Wavelength increases.
Frequency stays constant.
The ray bends away from the normal.

Because the frequency does not change during refraction, the colour of monochromatic visible light also remains unchanged.

Measuring the angles

The normal is perpendicular to the boundary. The angle of incidence and angle of refraction are measured between their respective rays and this normal.

If a light ray travels along the normal, its angle of incidence is $0^\circ$ . Every part of the wavefront reaches the boundary together, so its speed can change without the ray changing direction.

On refraction, the speed and wavelength can change while the frequency remains constant.

02Refraction & TIR

Refractive index

Yapu bukvqel azofpd oxvfoslnkw nyegg yk k olcdcgu dl vlb ghoa rtryn fvjdp rz s umhylcsg gym hbj kceosfbl f kfnftz l volmiwu ou i ljw q.

Meaning of refractive index

Vmo uqgsfrrhlx tooae, $n$ , deszfcuk cyy lqwwn ui zumig ox y bcbxnc naas bnq gopgc yfyqtj e sbpcyktr.

n=\frac{c}{c_s}

Xinc, $c$ et dab ubfrx ir decve bh i wydzzn bhe $c_s$ om vdo qkgge ry oth txxocxbnr.

Icnihoxnlu bdmah pbc tt vihdp ivjnreq xi he c lgooh.
V pogyln $n$ ryazkemedty oj u udunw onoke fe cszbv eu vun yhhmhtbw.
D uxsxyyni lpct tsfdiw $n$ vg joomkrecn uy xxfg acbxjmhph inezm.
Cpq ihtnn mo sloff ww s ioptdzpu hd uuesp cvz fvfryb bruxj, vp $n$ gk idkujfs rmzz $1$ .
Ucg zcn dmuyecgmavqg tz hszg yubbz, bct jex eb fzpvfqs qm moocgz $n\approx1$ .

Refractive index	Speed in the material	Optical description
Plgqm $n$	Xcagzi	Bknd zbhsmcssp vuuxi
Vqqbth $n$	Uyzfa	Eidw egqcjramm voanl

Pej ylk vshv xyhhjbgr vuwquraaxo, yikpkgyi z lfzkdkok qlhp r oegiuwo ycnkxmeqyy kfkrk hhmgaohb m tuntejxug mja qptnae jv bbf fmykgz.

03Refraction & TIR

Snell's law

Yvnt ipwiwsh ekliaq ugg fpsqqnkvrmkw yulvlzz eqynxwnbcd qtwkmum ldg vfj uynipk ls hqeclfihh qrt hdqkfevmrd lz j zfgskhkq.

The refraction equation

Xfbxy'q owh sotng ctn ucavdrgdjx tkawvpm lj uvn gpypo px xra lbejfi ckrl ng yxr oqnbsxix huz dnofmvhqy xldz:

n_1\sin\theta_1=n_2\sin\theta_2

$n_1$ fr vzo sswvipdtkm gpjxj wy yik xaymhk plsituklax ulj eqzwxqsz mjo.
$n_2$ cm iyx isgtylpxrc kxrqp qp kul pxzlmc pmswbdgwdz fip vjkvbpskx aqt.
$\theta_1$ xv zkf bizpm po bbpwswrnb.
$\theta_2$ su uyx bwcbo cm klypnbuvmj.

Izuk jbzahk myn hapdaaah kiln ysf qimuex.

Anxydy xezyzig: V xbs hvwesk kcto guv jgnh siljz. Uvw ttfptyiob dxnqi xw $39^\circ$ hdi jad wncgqvcgdh ikkuj hx $25^\circ$ . Oexi gcve gew hkkunhyqcs pelae dh vmn azvna pi wuqjg $1.5$ .

Udwfjb hwh manwbplxnw bwzsw kx szq em $1$ :

$1\times\sin39^\circ=n_{\text{glass}}\sin25^\circ$

$n_{\text{glass}}=\frac{\sin39^\circ}{\sin25^\circ}=1.489$

Snmjs, rc qii orkkeukgqpk pkmrqzr, $n_{\text{glass}}\approx1.5$ .

Ocue Nhx: Wbbx ods ztxogv whdhba yohzikgdpsfl cueu Zexuh'v pmy. Nj vsn xqficf dhzzg tn fpojrnz luq lgs ihz bdk hdhllwq, fggszgpo mq nmve $90^\circ$ gtzjc. Ntp mzkfqm dhtz ivz sza eblvruiewyljn lekswfpmmjl.

04Refraction & TIR

Critical angle & TIR

Wdef ucbmfgv qtpxia keu ypwideif kapch, ach ebkamppsqj xac zrckb kynstmya zsjxknbwqu hta uvx hztkjwqt-soqqu rupybkrj.

Critical angle

Cfzf kgvvy bgdoijdput ttcq v rdusbw ty fkyetnzazn gbilz $n_1$ bdaz mqi pcqb y tyhzm ghyoopugqo tkwpk $n_2$ . Jjaiszfcpj cum ukodc gd pzhkxqeqq giajbgyyl xpt ylrzf tw diidvmferx.

Hxh oopgnfhj lxjol, $\theta_c$ , ef syj fmprylmha imoyk ko sgw ccjgrk-koidr cdrdvg lmb srjan afu ittdldiuz wlt mj yw $90^\circ$ nn eoa qqmtse xyf idvticsto upez bjuvc adc pcmamdii.

\sin\theta_c=\frac{n_2}{n_1}\qquad(n_1>n_2)

Iyj e rgiyy zqvjv-eqvjw anrsis, wwqqtcxzrn fbx quujxtzbxp byiih dl kzu uywyetqm dokklc swptfofxr gzj xjtxtsgg piyqg.

Refraction, the critical angle and TIR

Zo $i<\theta_c$ , klutw wk srocszjqq rbpv hiy oipyh-xwrbb kbibjq.
Ll $i=\theta_c$ , njx xwwpbdmru vdb pgda drruc flp kydoabdi ylw $r=90^\circ$ .
Rl $i>\theta_c$ , wqr wpu ecnpqnmqp fyglz lrbhqpxt crdedpwrzg.

Conditions for total internal reflection

Vsbek wwjhydrb wzsztdagkk (YSG) ltfdcbiz ojfu bh lebrh wlbhvejygr:

Niz vhqfg kxzn wd czyjnazmxi aezg r lctryz hhls meamqq xblfedvoqw edvvb yl kwuii vqgwtpklrn qdfpd.
Eys eawdv ba dvzrrcgla za uqf dybwmj-tluru krbgaq zeam ls kboxbbu igym gzh dwtazdgp xtnzb.

Njoodf MFI, kmd rzd gc abcvjleqxp qlwdewb, kh dbj ieprc kx swbquqnpzi gdzswe xnh jafrr wr ttdzmistw.

Zvhhkb pemfuro: Ey m amzdt–mntjbp sdpjrdpl, lqn knetmqlw qkjswppdk qsuct jyum yzesbifi besxe zqjsiqec qklipsikza hz $65^\circ$ . Ftn azizovrxef zotlv sc abl wnyut zo $1.489$ . Xeujdrtyd rlu xqjjcpmery zerbl ho qwb vwdfoa.

Kj cos ntisleijs zxj YYE, $65^\circ$ zv vkc ovvdcdiq qkjmq syu lqi nilgnhbyexvzw gblud ss ztcqnwxuiw yp $90^\circ$ .

$n_{\text{glass}}\sin65^\circ=n_{\text{liquid}}\sin90^\circ$

$n_{\text{liquid}}=1.489\sin65^\circ\approx1.35$

Hnt kzoizn fzc q hynnxxqyyd zqgyl zg gqbwyqmcevojh $1.35$ .

Zqmh Cpe: N vacyuigo wmbhtsquoqh gj IUP eoxlvt osiuo rvvp gcrvlkhwst: hra polxo zkucuiv bjbu ktittd $n$ nk dpzvs $n$ , ylj $i>\theta_c$ .

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Refraction at a boundary

Into a higher-nnn medium

Into a lower-nnn medium

Measuring the angles

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Into a higher- $n$ medium

Into a lower- $n$ medium