Tonnau Waves PH 2 1 tameengr utexas edu

Tonnau (Waves) PH 2. 1

© tame@engr. utexas. edu Mae ton yn trosglwyddo (symud) egni o un lle i’r llall, ond nid yw’r cyfrwng sydd yn cario’r don yn symud i unrhywle.

© tame@engr. utexas. edu A wave transfers (moves) energy from one place to another, but the medium that carries the wave does not move to anyplace.

Dosbarthu tonnau …. . (1) tonnau ardraws neu donnau hydredol Mewn ton ardraws, mae’r gronynnau yn y cyfrwng yn osgiladu ar 90° i gyfeiriad yr egni yn symud Mewn ton hydredol, mae’r gronynnau yn y cyfrwng yn osgiladu yn ôl ac ymlaen ar hyd y cyfeiriad mae’r egni yn symud © Dr. Dan Russell

Classifying waves …. . (1) transverse waves or longitudinal waves In a transverse wave, the particles in the medium oscillate at 90° to the direction in which the energy travels © Dr. Dan Russell In a longitudinal wave, the particles oscillate backwards and forwards along the direction in which the energy travels

Dosbarthu tonnau …. . (2) tonnau mecanyddol neu donnau electromagnetig Mae’r mwyafrif o donnau yn donnau mecanyddol - maent angen cyfrwng (gronynnau) i gario’r don, e. e. tonnau sain © Tom Henderson Tonnau electromagnetig yw’r unig fath o donnau sy’n gallu symud trwy wactod (vacuum)

Classifying waves …. . (2) mechanical waves or electromagnetic waves The majority of waves are mechanical waves – they require a medium (particles) to carry the wave, eg sound waves © Tom Henderson Electromagnetic waves are the only type of waves that can travel through a vacuum

Dosbarthu tonnau …. . (3) tonnau cynyddol neu donnau unfan http: //www. abe. ufl. edu/ Mae ton gynyddol yn trosglwyddo egni i ffwrdd o’r ffynhonnell i gyfeiriad y don © Jim Richardson Nid yw ton unfan yn trosglwyddo egni i unrhywle – yn hytrach mae’r egni wedi ei ‘amgau’ ar bwyntiau ar hyd y don

Classifying waves …. . (3) progressive waves or standing waves http: //www. abe. ufl. edu/ A progressive wave transfers energy away from the source in the direction of the wave © Jim Richardson A standing wave does not transfer energy anywhere – the energy is ‘trapped’ at certain points along the wave

Disgrifio tonnau …. . Mewn gwaith Safon Uwch, mae nodweddion tonnau yn cael eu diffinio yn nhermau y gronynnau sydd yn y cyfrwng. Er enghraifft, ar gyfer ton ar sbring … dadleoliad osgled (1) Y dadleoliad (displacement) yw’r pellter fector mae gronyn wedi symud o’i fan gorffwys, (2) Yr osgled (amplitude) yw’r dadleoliad macsimwm

Describing waves …. . For work at Advanced Level, the properties of waves are defined in terms of the particles in the medium. For example, for a wave travelling along a spring … amplitude displacement (1) The displacement is the vector distance that the particle has moved from its rest position, (2) The amplitude is the maximum displacement

Disgrifio tonnau …. . tonfedd (3) Y tonfedd (wavelength) yw’r pellter rhwng y ddau ronyn agosaf sydd mewn gwedd (h. y. ar yr un pwynt yn eu mudiant cylch)

Describing waves …. . wavelength (3) The wavelength is the distance between the two nearest particles that are in phase (i. e. on the same point in their cycle)

Disgrifio tonnau …. . (4) Yr amledd (frequency) yw’r nifer o osgiliadau cyflawn mae gronyn yn gwblhau mewn 1 eiliad, (5) Y cyfnod (period) yw’r amser mae’n gymryd i ronyn gwblhau un osgiliad cyflawn. cyfnod 1 = amledd neu T = 1 f

Describing waves …. . (4) The frequency is the number of complete oscillations that a particle completes in 1 second, (5) The period is the time it takes for a particle to complete one oscillation. period 1 = frequency 1 or T = f

Disgrifio tonnau …. . (6) Buanedd ton (wavespeed) yw buanedd yr egni wrth iddo symud i ffwrdd oddi wrth y ffynhonnell buanedd = amledd × tonfedd

Describing waves …. . (6) The wavespeed is the speed at which the energy moves away from the source wavespeed = frequency × wavelength

Defnyddio graffiau i ddisgrifio tonnau … (1) graff dadleoliad-pellter dadleoliad © Tree. Hugger. com 2008 pellter • ciplun (snapshot) o holl arwyneb ton ar un amser arbennig, • gellir mesur yr osgled a’r tonfedd yn syth oddi ar y graff

Using graphs to describe waves … (1) a displacement-distance graph displacement © Tree. Hugger. com 2008 distance • it is a snapshot of the whole wave surface at one particular time, • the amplitude and wavelength can be measured directly from the graph

Defnyddio graffiau i ddisgrifio tonnau … (2) graff dadleoliad-amser …. . yn dangos sut mae dadleoliad un pwynt ar arwyneb y don yn amrywio gydag amser dadleoliad © Tree. Hugger. com 2008 amser • gellir mesur yr osgled a’r cyfnod yn syth oddi ar y graff

Using graphs to describe waves… (2) a displacement-time graph …. shows how the displacement of one point on the surface of the wave changes with time displacement © Tree. Hugger. com 2008 time • the amplitude and period can be measured directly from the graph

Beth yw’r berthynas rhwng y ddau graff? graff dadleoliad-pellter (‘llun’ o’r don o’r ochr) dadleoliad graff dadleoliad-amser ar gyfer pwynt P dadleoliad P pellter amser • wrth i’r don symud i’r dde, mae’r siâp yn symud drwy bwynt P • mae pwynt P yn codi yn raddol ac yna’n disgyn yn sydyn • mae un graff yn ddelwedd-drych o’r llall

How are the two graphs related? displacement-distance graph (a side-view of the wave) displacement-time graph for point P displacement P distance time • as the wave moves to the right, the shape passes through point P • point P rises slowly and then falls quickly • one graph is a mirror-image of the other

Yr Egwyddor Arosod (The Principle of Superposition) “Pan mae mwy nac un ton yn cyfarfod, dadleoliad y don cydeffaith yw swm fector dadleoliadau y tonnau unigol” tonnau yn symud i’r un cyfeiriad tonnau yn symud i gyfeiriadau croes

The Principle of Superposition “When two or more waves meet at a point, the resultant displacement is the vector sum of the displacements of the individual waves” waves moving in the same direction waves moving in opposite directions

Y tanc crychdonni (the ripple tank) dŵr bas padl yn osgiladu trochwr www. ddart. net cysgod y crychdonnau ar y llawr

The ripple tank shallow water an oscillating paddle dipper www. ddart. net the ripples cast a shadow on the floor

http: //www. 555 electronics. com. au/ Mae tanc crychdonni gyda dau drochwr yn cael ei ddefnyddio i ddangos tonnau ar ddŵr yn ymyrryd gyda’i gilydd. Mae patrwm ymyriant sefydlog ar wyneb y dŵr … ymyriant adeiladol (tonnau yn symud) ymyriant dinistriol (yn llonydd) http: //www. 555 electronics. com. au/

A ripple tank with two dippers is used to show the interference of waves on water There is a stable interference pattern on the water surface … constructive interference (moving waves) destructive interference (no movement of water) http: //www. 555 electronics. com. au/

Ymyriant tonnau (interference of waves) Mae patrwm ymyriant sefydlog yn ffurfio pan mae dwy don gyda’r un amledd ac osgled yn arosod. Mae’n rhaid i’r tonnau fod yn gydlynol (coherent) – mae ganddynt yr un amledd ond nid ydynt o reidrwydd mewn gwedd.

Interference of waves A stable interference pattern is observed when two waves with the same frequency and amplitude superpose. The waves must be coherent – they have the same frequency but are not necessarily in phase

Mae ymyriant adeiladol yn digwydd pan mae tonnau yn cyrraedd pwynt mewn gwedd h. y. dau frig neu dau gafn yn cyfarfod Mae ymyriant dinistriol yn digwydd pan mae tonnau yn cyrraedd pwynt mewn gwrthwedd h. y. brig a cafn yn cyfarfod

Constructive interference takes – place when waves reach a point in phase i. e. the meeting of two peaks or two troughs Destructive interference takes place when waves reach a point in antiphase i. e. the meeting of a peak and a trough

http: //www. ngs ir. netfirms. com /englishhtm/Int erference. htm Pwyswch y botwm ar y chwith, yna cliciwch ar unrhyw ran o’r patrwm ymyriant i weld y gwahaniaeth llwybr animeiddiad Mae’r math o ymyriant sydd yn digwydd ym mhwynt P yn dibynnu ar y gwahaniaeth llwybr o’r ddwy ffynhonnell i bwynt P: P A B ymyriant adeiladol os yw …. . | AP – BP | = nλ ymyriant dinistriol os yw …. . | AP – BP | = (n+½)λ

http: //www. ngs ir. netfirms. com /englishhtm/Int erference. htm Press the button on the left, then click on any part of the interference pattern to view the path difference animation The type of interference that takes place at P depends on the path difference from the two sources to point P: P A B constructive interference if. . | AP – BP | = nλ destructive interference if. . . | AP – BP | = (n+½)λ

Er mwyn cael ymyriant adeiladol, mae’n rhaid i’r tonnau o A a B gyrraedd pwynt P mewn gwedd … gwahaniaeth llwybr = sero gwahaniaeth llwybr = 2λ gwahaniaeth llwybr = 3λ

For constructive interference to occur, the waves from A and B must reach point P in phase … path difference = zero path difference = λ path difference = 2λ path difference = 3λ

Er mwyn cael ymyriant dinistriol, mae’n rhaid i’r tonnau o A a B gyrraedd pwynt P mewn gwrthwedd … gwahaniaeth llwybr = 1/2λ gwahaniaeth llwybr = 3/2λ gwahaniaeth llwybr = 5/2λ gwahaniaeth llwybr = 7/2λ

For destructive interference to occur, the waves from A and B must reach point P in antiphase … path difference = 1/2λ path difference = 3/2λ path difference = 5/2λ path difference = 7/2λ

Mae ymyriant adeiladol yn digwydd pan mae’r gwahaniaeth llwybr yn hafal i nifer gyfan o donfeddi … | AP – BP | = nλ ble mae n = 0, 1, 2, 3, …. .

Constructive interference occurs when the path difference is equal to a whole number of wavelengths… | AP – BP | = nλ where n = 0, 1, 2, 3, …. .

Mae ymyriant dinistriol yn digwydd pan mae’r gwahaniaeth llwybr yn hafal i nifer gyfan o hanner tonfeddi … | AP – BP | = (n+½)λ ble mae n = 0, 1, 2, 3, …. .

Destructive interference occurs when the path difference is equal to a whole number of half-wavelengths… | AP – BP | = (n+½)λ where n = 0, 1, 2, 3, …. .

Ymyriant tonnau sain (1) defnyddio dau ddarseinydd a generadur signal 500 Hz animeiddiad sain i fewn sain allan www. practicalphysics. org (2) defnyddio tiwb Quincke mae un ochr i’r tiwb yn llithro i fewn ac allan fel braich trombon, fel bod hyd un o’r llwybrau yn newid – felly mae lefel y sain allbwn yn newid

Interference of sound waves (1) using two loudspeakers and a signal generator 500 Hz animation sound in sound out www. practicalphysics. org (2) using Quincke’s tube One side of the tube can slide inwards and outwards like the arm of a trombone, such that the length of one path is changed – hence the level of the ouput varies

Defnyddio ymyriant tonnau sain i leihau lefelau sŵn …. . sŵn gwreiddiol tonnau wedi eu cyfuno meicroffon ton wedi ei gwrthdroi © 20 th. Century. Voice

Using the interference of sound waves to reduce noise level …. . original noise combined wave microphone the inverted wave © 20 th. Century. Voice

groups. physics. umn. edu Ymyriant microdonnau (yr un theori ag arbrawf hollt-ddwbl Young gyda goleuni - gweler sleidiau yn bellach ymlaen) 10 cm derbynnydd 20 cm hollt-ddwbl trawsyrrydd λ~6 cm darseinydd signal drydanol o’r derbynnydd yn cael ei fwydo i’r darseinydd groups. physics. umn. edu symud y derbynnydd yn ôl ac ymlaen ar hyd y linell yma i gael signal uchel (ymyriant adeiladol) a signal isel (ymyriant dinistriol)

Interference of microwaves groups. physics. umn. edu (the same theory as Young’s double-slit experiment with light – see later slides 10 cm receiver 20 cm transmitter λ~6 cm loudspeaker an electrical signal from the receiver is fed into the loudspeaker groups. physics. umn. edu the receiver is moved backwards and forwards along this line to obtain a large signal (constructive interference) and a low signal (destructive interference) double-slit

Ton unfan (stationary wave or standing wave) © RBCybernetics 2006 Mae ton unfan yn ffurfio pan mae dwy don sydd yr un fath yn symud gyda’r un buanedd i gyfeiriadau croes i’w gilydd yn arosod

Standing wave © RBCybernetics 2006 A standintg wave is formed when two identical waves that are travelling at the same speed in opposite directions superpose

gwrthnodau – y dadleoliad mwyaf © Orbiting. Frog nodau – dim dadleoliad pellter rhwng dau nod = ½λ

antinodes – maximum displacements © Orbiting. Frog nodes – no displacement distance between two nodes = ½λ

Ton ardraws unfan – arbrawf Melde © Antonine. Education dirgrynydd llinyn ysgafn (tua 3 m) pont symudol pwli masiau http: //www. n gsir. netfirms. com/english htm/Stat. Wav e. htm animeiddiad Mae’r llinyn yn dirgrynu gydag osgled uchel ar rai amleddau yn unig pan mae hyd y llinyn = nλ/2. Ar bob amledd arall, mae’r dirgryniad yn fychan iawn.

Standing transverse wave - Melde’s experiment © Antonine. Education vibrator a light string (~ 3 m) moveable bridge pulley masses http: //www. n gsir. netfirms. com/english htm/Stat. Wav e. htm animation The string oscillates with large amplitudes at some frequencies only when the length of the string = nλ/2. At all other frequencies, the vibration is very small

Ton hydredol unfan – tiwb Kundt © Antonine. Education ½λ mae’r powdwr yn cael ei wthio i’r pwyntiau ble mae’r aer yn ‘llonydd’ © R Nave - Hyper. Physics

Standing longitudinal wave – Kundt’s tube loudspeaker antinodes © Antonine. Education nodes ½λ light powder the powder is pushed to regions where the air is ‘still’ © R Nave - Hyper. Physics

Ton hydredol unfan – tiwb Ruben ton sain unfan yn cael ei chreu mewn nwy fflamadwy © Gadget. Venue. com nwy yn llosgi gorchudd rwber tiwb metel gyda thyllau generadur signal nwy fideo

Standing longitudinal wave – Ruben’s tube a standing sound wave is produced in a flammable gas © Gadget. Venue. com burning gas rubber cover metal tube with regularly-spaced holes signal generator gas video

Diffreithiant …. . pan mae ton yn rhyngweithio gyda rhwystr sydd yn ei llwybr yn troi o amgylch rhwystr yn gwasgaru ar ôl symud trwy fwlch © Lorenzarius 2005

Diffraction … when a wave interacts with some obstacle in its path spreading around an obstacle spreading after passing through a gap © Lorenzarius 2005

Defnyddio’r tanc crychdonni i ddangos diffreithiant … trwy fwlch o amgylch rhwystr http: //www. ngsir. netfirms. com/en glishhtm/Diffracti on. htm © cams. njit, edu http: //www. n gsir. netfirms. com/english htm/Diffracti on 3. htm

Using the ripple tank to show diffraction … through a gap around an obstacle http: //www. ngsir. netfirms. com/en glishhtm/Diffracti on. htm © cams. njit, edu http: //www. n gsir. netfirms. com/english htm/Diffracti on 3. htm

Mae diffreithiant yn digwydd orau pan mae’r rhwystr un ai tua’r un maint neu yn llai na’r tonfedd rhwystr λ © www. ngir. netfirms. com

Diffraction is most noticeable when the obstacle is either approximately the same size or smaller than the wavelength obstacle λ © www. ngir. netfirms. com

Polareiddio goleuni Dychmygwch don ardraws yn symud allan o’r sgrin … gyda’r dirgryniadau ym mhob plân … Yn gyffredinol … nid yw’r tonnau wedi eu polareiddio

Polarisation of light Imagine a transverse wave moving out from the screen … with the vibrations in all of the planes … In general … the waves are not polarised

Defnyddio hidlen Polaroid™ i bolareiddio goleuni … goleuni heb ei bolareiddio goleuni wedi ei bolareiddio … goleuni sydd yn dirgrynu mewn un plân yn unig sydd yn gallu pasio trwy Polaroid™ I gymharu … mae’n rhaid i’r raff ddirgrynu i’r un cyfeiriad â’r holltau os yw’r don i basio drwy’r ffens © Tom Henderson

Using a Polaroid™ filter to polarise light … unpolarised light … only light that vibrates in one particular plane passes through Polaroid™ In comparison … the rope must vibrate in the same direction as the slats if the wave is to pass through the fence © Tom Henderson

Defnyddio ail hidlen Polaroid™ … goleuni heb ei bolareiddio wedi ei bolareiddio animeiddiad wedi ei bolareiddio ac yn ei chylchdroi … goleuni heb ei bolareiddio wedi ei bolareiddio © Heriot-Watt University 2001

animation Using a second Polaroid™ filter … unpolarised light and rotating it … unpolarised light © Heriot-Watt University 2001

Ymyriant goleuni – a ydyw yn digwydd? Lamp goleuni gwyn Pob lliw gyda’i amledd arbennig ei hun Dim gwahaniaeth gwedd cyson rhwng tonnau o liwiau gwahanol Lamp goleuni monocromatig (h. y. un lliw) Pob ton gyda’r un amledd, ond mae’r lamp yn cynhyrchu tonnau ar hàp. Dim gwahaniaeth gwedd cyson

Do light waves interfere? Lamp prducing white light All colours have different frequencies. The phase difference between waves of different colours is not constant. Lamp producing monochromatic light (i. e. one colour) Each wave has the same frequency, but the lamp produces waves at random. The phase difference is not constant

Arbrawf hollt-ddwbl Young tonnau o S 2 ac S 3 yn ymyrryd â’i gilydd S 2 S 1 S 3 tonnau mewn gwedd ac yn diffreithio animeiddiad patrwm sefydlog ar y sgrin © http: //homepage. univie. ac. at/Franz. Embacher/Kinder. Uni 2005/waves. gif

Young’s double-slit experiment waves from S 2 and S 3 interfere S 2 S 1 S 3 waves are in phase and are diffracting animation a stable pattern on the screen © http: //homepage. univie. ac. at/Franz. Embacher/Kinder. Uni 2005/waves. gif

Arbrawf hollt-ddwbl Young Mae patrwm sefydlog ar y sgrin www. studyphysics. ca ediau llachar ond … (1) mae’r ediau yn agos iawn at ei gilydd (felly mae angen symud y sgrin yn bellach oddi wrth yr holltau dwbl) (2) mae arddwysedd y patrwm yn isel

Young’s double-slit experiment There is a stable pattern on the screen www. studyphysics. ca bright eddies but … (1) the eddies are very close together (so the screen needs to be moved further away from the slits) (2) the intensity of the pattern is low

Arbrawf hollt-ddwbl Young – defnyddio laser tua½mm rhwng yr holltau 3 -4 m LASER tonnau mewn gwedd www. juliantrubin. com/bigten/youngdoubleslit. html mae’r sleid ar flaen y laser yn hollti’r paladr yn ddau ran

Young’s double-slit experiment – using a laser about mm between the slits 3 -4 m LASER waves in phase www. juliantrubin. com/bigten/youngdoubleslit. html the slide in front of the laser splits the beam into two parts

Wrth ystyried y goleuni sydd yn cyrraedd dau edi cyfagos … o’r triongl melyn, sinθ = λ / a y θ a o’r triongl glas, tanθ = y / D θ D gwahaniaeth llwybr = λ Os yw D» a, mae sinθ ≈ tanθ, felly … neu y = λD a y D = λ a y pellter rhwng dau edi cyfagos

Considering the light that reaches two adjacent bright eddies …. . from the yellow triangle, sinθ = λ / a θ a from the blue triangle, tanθ = y / D θ y D path difference = λ If D» a, sinθ ≈ tanθ, therefore … or y = λD a y D = λ a the distance between adjacent eddies

Ymyriant mewn ffilmiau tenau (thin film interference) O ble ddaw y lliwiau? http: //micro. ma gnet. fsu. edu/pri mer/java/interfe rence/soapbub bles/index. html © © R Nave - Hyper. Physics © exploratorium. com

Thin film interference Why do the colours appear? http: //micro. ma gnet. fsu. edu/pri mer/java/interfe rence/soapbub bles/index. html © R Nave - Hyper. Physics © exploratorium. com

mae pelydryn 1 wedi adlewyrchu oddi ar wyneb uchaf yr haen denau, ac mae’r pelydryn 2 yn adlewyrchu oddi ar waelod yr haen. Mae’r lliwiau i’w gweld pan mae pelydrau 1 a 2 yn ymyrryd gyda’i gilydd: ymyriant adeiladol (y lliw i’w weld yn y gymysgedd): gwahaniaeth llwybr = nλ ymyriant dinistriol (y lliw ar goll o’r gymysgedd): gwahaniaeth llwybr = (n+½)λ

Ray 1 has reflected from the upper surface of the thin film, and ray 2 has reflected from the lower surface. The colours are seen when rays 1 and 2 interfere: constructive interference (the colour is visible in the mixture): path difference = nλ destructive interference (the colour is missing from the mixture): path difference = (n+½)λ

Goleuni’n diffreithio Pan mae goleuni yn symud trwy hollt denau iawn mae’n diffreithio: © www 1. union. edu

Diffraction of light Light diffracts when it travels through a very narrow slit : © www 1. union. edu

Mae patrwm diffreithiant mwy amlwg i’w gael wrth ddefnyddio gratin diffreithiant … patrwm cyson o linellau paralel wedi eu crafu ar wydr mae’r pellter rhwng dwy linell tua’r un maint â thonfedd goleuni

The diffraction pattern is more apparent when a diffraction grating is used … a regular pattern of parallel lines scratched onto glass the distance between two lines is approximately the size of the wavelength of light

Pan mae goleuni yn teithio drwy’r gratin diffreithiant mae pelydrau yn diffreithio i sawl cyfeiriad. Mae’r pelydrau yma yn ymyrryd (fel yn yr arbrawf hollt-ddwbl) … ond mae’r macsima yn fwy clir gyda’r gratin diffreithiant © www 1. union. edu patrwm trwy gratin patrwm trwy hollt ddwbl

When light passes through the diffraction grating it diffracts outwards. The diffracted rays then interfere (as it does in the double-slit experiment) … but the maxima are clearer when the grating is used © www 1. union. edu pattern through a grating pattern through the double-slit

Ar gyfer y pelydrau sy’n diffreithio trwy ongl θ … ‘d’ yw’r pellter rhwng dwy hollt gyfagos ar y gratin d B A pellter AB = d·sin I’r pelydrau gyrraedd y linell mewn cydwedd, gwahaniaeth llwybr rhwng dau belydryn cyfagos = d·sinθ

For the rays diffracting through an angle θ … ‘d’ is the distance between adjacent slits in the grating d B A distance AB = d·sin For the rays to reach this line in phase, the path difference between adjacent rays = d·sinθ

trefn sero n=0 n=1 ← trefn gyntaf n=2 n=3 pellter rhwng dwy linell yn y gratin ar gyfer unrhyw drefn … θ n=2 ← ail drefn n=3 ongl rhwng y drefn a threfn sero d·sinθ = nλ

zero order n=0 n=1 ← first order n=2 n=3 distance between two lines in the grating for any order … θ n=2 ← second order n=3 angle between the order and zero order d·sinθ = nλ

Mae θ ar gyfer pob trefn yn dibynnu ar λ …. . n=3 n=2 n=1 n=0 n=1 n=2 n=3

For each order, θ depends on λ …. . n=3 n=2 n=1 n=0 n=1 n=2 n=3

Felly mae’r gratin yn gwahanu lliwiau …. . n=3 λ mawr → θ mawr n=2 λ llai → θ llai n=1 n=0 – cymysgedd o oleuni coch a gwyrdd n=1 n=2 n=3

Therefore the grating is able to separate colours …. . n=3 large λ → large θ n=2 n=1 smaller λ ↓ smaller θ n=0 – mixture a mixture of red and green light n=1 n=2 n=3

Nid oes rhaid i’r lliwiau fod bob-yn-ail …. . n=3 n=4 θ ar gyfer n=3 coch yn fwy na θ n=3 n=2 ar gyfer n=4 fioled! n=2 n=1 n=0 – cymysgedd n=1 cymysgedd o oleuni coch a fioled n=1 n=2 n=3 n=4 n=3

The colours do not have to alternate …. . n=3 n=4 n=3 n=2 θ for red n=3 is greater than θ for violet n=4! n=2 n=1 n=0 – mixture n=1 a mixture of red and violet light n=1 n=2 n=3 n=4 n=3

Defnyddio sbectromedr i fesur λ yn fanwl-gywir yn mesur yr ongl i’r 0. 1 agosaf lamp i gynhyrchu pelydryn tenau o oleuni © 1996 Dr. H. K. Ng

Using a spectrometer to measure λ accurately magnifying glass and vernier scale measuring the angle with a resolution of 0. 1 © 1996 Dr. H. K. Ng slit lamp rotating telescope collimator to produce a narrow beam of light