Interference is when two (or more) sets of waves meet and combine to produce a new pattern.

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1 Interference Interference is when tw (r mre) sets f waves meet and cmbine t prduce a new pattern. This pattern can vary depending n the riginal wave directin, wavelength, amplitude, etc. The tw mst extreme effects f interference are shwn belw: Cnstructive interference Tw sets f waves meet in phase. Tw crests meet r tw trughs meet t prduce a larger crest r trugh. Destructive interference Tw sets f waves meet cmpletely ut f phase, i.e. 180 ut f phase. A crest meets a trugh and cmbine t cancel each ther ut and prduce n wave at that pint. Cherent surces Tw surces are cherent if they have a cnstant phase difference. They will have the same frequency. They ften have the same amplitude. Fr light, cherent surces can be prduced frm splitting a single surce int multiple surces, e.g. using a duble-slit r a diffractin grating (further details prvided belw).

2 Interference is the test fr wave-like prperties Anything that prduces interference is said t have wave-like prperties Sund can prduce interference effects s has wave-like prperties Electrmagnetic radiatin can prduce interference effects s has wave-like prperties Hwever, phtns display particle-like prperties in the phtelectric effect Interestingly, electrns have been made t prduce interference effects, therefre they have wave-like prperties Hwever, electrns display particle-like prperties when they are used in scattering experiments since they cllide and scatter the way all particles d The thery and bservatin f phtns, electrns etc. displaying bth wave-like and particlelike prperties is called wave-particle duality Pint surce A pint surce is a surce f energy, such as light r sund, which can be regarded as having negligible dimensins. Mnchrmatic surce A surce is said t be mnchrmatic if it has ne single frequency A helium-nen (red) laser is an example f a mnchrmatic surce A halgen light bulb emitting white light is nt a mnchrmatic surce

3 Interference f water waves If tw pint surces prduce tw sets f circular waves, they will verlap and cmbine t prduce an interference pattern. The semicircular lines represent crests; the trughs are between the crests. S 1 and S 2 are cherent pint surces, i.e. the waves are prduced by the same vibratr and cme frm a single pint and spread ut in all directins. X O = pint f cnstructive interference. = pint f destructive interference. = line f cnstructive interference = line f destructive interference. The pints f cnstructive interference frm waves with larger amplitude and the pints f destructive interference prduce calm water. The psitins f cnstructive interference and destructive interference frm alternate lines which spread ut frm between the surces. As yu mve acrss a line parallel t the surces, yu will therefre encunter alternate large waves and calm water. Interference frm ne set f waves It is pssible t prduce interference frm ne surce f waves by divisin f the wavefrnt. Plane waves are made t pass thrugh tw small gaps (similar in size t the wavelength) t prduce tw cherent surces f circular waves by diffractin. These will then prduce an interference pattern as shwn abve with water waves.

4 Interference f light Tw surces f cherent light are needed t prduce an interference pattern. Tw separate light surces such as lamps cannt be used t d this, as there is n guarantee that they will be cherent, i.e. have the same phase difference. Tw cherent surces are prduced frm ne mnchrmatic (single frequency) surce using the principle abve. As stated abve, a laser is a mnchrmatic surce. Alternate series f light and dark lines (fringes). Light fringe, arrive in phase, cnstructive interference. Dark fringe, arrive ut f phase, destructive interference. Path difference and interference An interference pattern is mre easily explained in terms f path difference. Cnsider an interference pattern prduced by tw cherent wave surces as belw.

5 The central, r zer rder maximum has zer path difference, i.e. bth surces have travelled the same distance t reach this pint. As yu mve acrss the pattern away frm the zer rder, the first rder maximum is reached. This is the next pint where the waves arrive in phase; the waves here have a path difference f 1, the waves frm ne surce have travelled 1 further than the waves frm the ther surce. Cnstructive interference ccurs and a maximum is prduced. Similarly, the path difference t the secnd rder maximum wuld be 2 and s n. The first minimum bserved, i.e. the minimum next t the central maximum, is reached at the first pint the waves arrive ut f phase; the waves here have a path difference f 1 2. Destructive interference ccurs and a minimum is prduced. Similarly, the path difference t the next minimum wuld be 3 and s n. 2 In general: Fr a maximum path difference, S 2 P S 1 P = m Whle number f Fr a minimum path difference, S 2 P S 1 P = (m ) Odd number f 1 2. The term rder fr a maximum r minimum is simply the value f m in the abve equatins. Fr a maximum this is straightfrward. When m = 0 we have the central maximum. When m = 1 we have the first maximum. Hwever, fr a minimum sme care is required. The first minimum, i.e. the minimum next t the central bright band, is the zer rder minimum with m = 0 and a path difference f 1 2

6 Example (a) Distances AC and BC are 51 cm and 63 cm respectively. Pint C is the third rder maximum. Determine the wavelength f the surce. Path difference BC AC = 12 cm. Fr third rder maximum, path difference = 3. path difference = m cm (b) If the abve surce was replaced by anther with wavelength 8 cm, what effect wuld be bserved at pint C? If = 8 cm then Path difference BC AC = 12 cm, as befre. path difference Therefre destructive interference wuld nw be bserved at pint C and a minimum (n light) wuld be seen.

7 The grating and mnchrmatic light A grating cnsists f many equally spaced slits psitined extremely clse tgether (e.g. 300 lines per mm). Light is diffracted thrugh each slit and interference takes place in a similar fashin t the duble slit. The advantage f the grating is that much mre light is transmitted thrugh and a clearer interference pattern is seen. Grating equatin Fr a grating: d sin m Where: m = rder f the maximum (1,2,3 ) = wavelength f light (m) d = separatin f slits (m) = angle frm zer rder t maximum m (). If the abve frmula is rearranged t sin = m, then it can be seen that the fllwing will d increase the separatin f the maxima: increase the wavelength, i.e. mve frm blue twards red light decrease the slit separatin (d), i.e. have mre lines per mm. Als ntice that mving the screen further away will als increase the separatin f the maxima.

8 Example A diffractin grating with 300 lines per mm is used t prduce an interference pattern. The secnd rder maximum is btained at a diffracted angle f 19. Calculate the wavelength f the light. Step 1 calculate slit separatin d using the quted number f lines per mm 1 d m d = m m = 2 = 19 dsin m d sin m sin(19 ) m (r 540 nm) Using a grating t measure wavelength The setup shwn n the previus page can be used t measure the wavelength f the light surce. The angle between the central maximum and the chsen maximum can be determined frm tan = x/d, where x is the distance frm the central maximum t the chsen maximum, and D is the distance frm the grating t the screen, i.e. where the pattern is bserved. x D

9 Apprximate values f wavelengths f visible light Red 700 mm = m Green 540 nm = m Blue 490 nm = m. Grating and white light It is pssible t use a grating t bserve the interference pattern btained frm a white light surce. Since white light cnsists f many different frequencies, the fringe pattern prduced is nt as simple as that btained frm mnchrmatic light. Explanatin The central fringe is white because at that psitin, the path difference fr all wavelengths present is zer, therefre all wavelengths will arrive in phase. The central fringe is therefre the same clur as the surce (in this case, white). The first maximum ccurs when the path difference is 1. Since blue light has a shrter wavelength than red light, the path difference will be smaller, s the blue maximum will appear clser t the centre. Each clur will prduce a maximum in a slightly different psitin and s the clurs spread ut int a spectrum. m These effects can als be explained using the frmula dsin = m r sin. d If d and n are fixed, the angle depends n the wavelength. S, fr any given fringe number, the red light, with a lnger wavelength, will be seen at a greater angle than the blue light.

10 Cmparing spectra frm prisms and gratings Only ne spectrum prduced. Red deviated least, vilet the mst. Bright images. Usually less widely spaced (dispersed). Many spectra prduced, symmetrical abut the central maximum. Red deviated mst, vilet the least. Less intense energy divided between several spectra. Usually mre spread ut. Central image always the same clur as the surce.

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