VISUAL PHYSICS ONLINE MODULE 7 NATURE OF LIGHT POLARISATION View vide n plarisatin f light While all the experimental evidence s far that supprts the wave nature f light, nne f it tells us whether light is a lngitudinal r transverse wave. Lngitudinal waves are characterised by mtin f the particles f the medium parallel t the directin in which the waves travel, e.g. sund waves in air. Fig. 1. Lngitudinal sund wave in air.
Transverse waves are characterised by the mtin f the particles f the medium perpendicular t the directin in which the waves are prpagating, e.g. vibratins f a guitar string. Fig. 2. Transverse wave alng a string. Reflectin, refractin, diffractin, interference ccur in the prpagatin f bth transverse and lngitudinal waves. A definitive distinctin between lngitudinal and transverse waves may be made based upn the capacity t be plarised. A linearly (plane) plarised beam f transverse waves is ne whse vibratins ccur in nly a single directin perpendicular t the directin f prpagatin f the wave, s that the entire mtin in which the beam travels is cnfined t a plane called the plane f plarisatin.
Fig. 3. Linearly r plane plarized light. When many different directins f plarisatin are present in a beam f transverse waves, ften with vibratins ccurring equally in all directins perpendicular t the directin f prpagatin, the beam is said t be unplarised. Fig. 4. Unplarized light beam cnsists f vibratins in many planes perpendicular t the directin f prpagatin.
Since the vibratins cnstituting a lngitudinal wave can nly take place in ne directin in the directin f prpagatin, lngitudinal waves cannt be plarised. By establishing whether light can be plarised r nt, then, we have a means fr determining the type f wave - lngitudinal r transverse. We can shw experimentally that light is a transverse wave by using a micrwave beam incident upn a metal grid as shwn in figure 5. A typical wavelength f a micrwave beam is abut 3 mm. Prvided the vertical metal grid spacing is smaller than the wavelength, when the grid intercepts the micrwaves nly the micrwaves that are perpendicular t the vertical metal grid are transmitted.
Fig. 5. Actin f vertical metal grid wire grid n an unplarised micrwave beam. Effective absrptin f all vertical cmpnents f the radiatin ccurs when grid spacing. The scillatin f the electric field fr the micrwave beam can induce electric currents in the metal grid when the grid and electric field are parallel t each ther, and the energy will be absrbed frm the beam. That is, the free electrns in the metal are set int scillatry mtin and these currents dissipate energy as thermal energy.
Als, these scillating electrns radiate electrmagnetic energy in all directins, except in the directin f the scillatin and in the frward directin there is a cancellatin f the incident and radiated waves. The main reasn fr the disappearance f the transmitted wave is the destructive interference between the incident and generated wave. When the plane f scillatin f the electric field is perpendicular t the metal grid, minimum absrptins ccurs and the beam will pass thrugh the grid with zer r little attenuatin prvided grid spacing as shwn in figure 6. When the grid and electric field are riented perpendicular t each ther, appreciable scillatins f the free electrns cannt ccur and s there is little cancellatin between the incident and generated wave.
Fig. 6. Experiments with micrwaves and a metal grid prvides cnclusive evidence that micrwaves are transverse waves because they exhibit plarisatin behaviur.
The rientatin f any linearly (plane) plarised beam can be expressed in terms f its X, Y and Z cmpnents. Figure 7 shws an incident micrwave beam with electric field Ex, E y,0. When the grid is riented in the Y directin, the vertical cmpnent E y is absrbed and nly the hrizntal cmpnent E x is transmitted. Fig. 7. Only cmpnents f the electric field that are perpendicular t the grid are transmitted.
The dr f a micrwave ven has a metal mesh embedded in it. S, zer micrwave radiatin can pass thrugh the dr, because all cmpnents f the electric field will be absrbed by the metal grid. Fig. 8. Fr safety reasns, a micrwave ven has a metal mesh embedded int its dr s that there is zer transmissin f the micrwave radiatin thrugh it.
A gd example f the use f plarisers are the plarid lens in sunglasses. Plarid is an artificially made plarising material. It cnsists f tw plastic sheets with a thin layer f needle-like quinine idsulfate crystals between them. The crystals are aligned using a very strng electric field and the resulting clear material transmits nly light in a single plane f plarisatin. In sunglasses, the crystals are aligned hrizntally s that they strngly absrb the cmpnents f the light in the hrizntal directin cmpared t the vertical directin (figure 9). Fig. 9. Plarid sunglasses have plarid lens that are strng absrbers f the cmpnent f the electric field rientated in the hrizntal plane.
When light strikes a nn-metallic surface at any angle ther than the perpendicular, the reflected beam is plarised preferentially in the plane parallel t the surface (figure 10). Fig. 10. Light reflected frm a nn-metallic surface is plarised with its plane f plarisatin parallel t the surface. Plarid sunglasses are made s that the vertical cmpnent f the electric field is preferentially transmitted t eliminate the mre strngly reflected hrizntal cmpnent. S, wearing plarid sunglasses will reduce the glare (figure 11). Fishermen were Plarids t reduce reflected glare frm the surface f water and thus see beneath the water mre clearly.
Fig. 11. Light reflected frm a nn-metallic surface is partially plarised parallel t the surface. Plarid sunglasses preferentially absrb the hrizntal cmpnent f sunlight, thus reducing the glare.
Phtelasticity When transparent materials are placed between tw plarises, clurful stress patterns are bserved (figure 12). Very cmplicated stress distributins can be analysed by these ptical methds. Fig. 12. Stress patterns in transparent materials are revealed by because light is a transverse wave and can be plarised.
Malus s Law fr plarised light We will cnsider the experimental arrangement f shining unplarised light thrugh a pair f Plarid sheets which are labelled the Plariser and Analyser. The transmitted light is detected by a Phtcell as shwn in figure 13. The Phtcell measures the intensity f the light transmitted t it. The intensity f the light is prprtinal t the square f the electric field f the light (1) I E 2 The Plariser is adjusted s the light passing frm the Plariser t the Analyser is linearly plarized with a vertical plane f plarisatin. S, the Plariser has its plarising axis (transmissin axis) in the vertical directin. Fr an ideal plarising filter, the transmitted intensity is half the incident intensity (50% f the radiatin absrbed because nly ne cmpnent f the electric field is transmitted thrugh the filter). The Analyser can be rtated abut the axis f the ptical system and the angle f its plarising axis is measured w.r.t. the vertical. The Analyser is rtated and set t the psitin t give a maximum intensity I as measured by the Phtcell max detectr. This psitin will have the plarising axis f the Analyser in the vertical directin and the angle between the
Analyser s plarising axis and the vertical is 0. The angle f the Analyser is then set t as shwn in figure 13. The incident electric field fr the Analyser is E E ˆj. The cmpnent f the electric field transmitted frm the Analyser t the Phtcell is E cs. Thus, using equatin 1, the light intensity transmitted thrugh the Analyser gives Malus s Law fr plarised light passing thrugh an Analyser (2) I I cs 2 max Equatin 2 was discvered experimentally by E.L. Malus in 1809. Malus s Law applies nly if the incident light passing thrugh the Analyser is already linearly plarised. Exercise 1 Draw tw graphs t test Malus s Law fr the Analyser angle 180 180 when the light incident upn the Analyser is linearly plarized. At what angle is the intensity a maximum? At what angles is there extinctin f the light thrugh the filter? At what angle is the Analyser set t reduce the intensity t 50% f its maximum value?
Slutin Yu cannt make definite mathematical cnclusins abut curved lines. If pssible, yu need t plt the data t get a straight line. In this case we can d this by pltting the graph f 2 I vs cs.
The maximum intensity is 10 a.u. and this ccurs at the angle 0. Zer light passes thrugh the ideal filter at the angles 90. The intensity drps t 50% f its maximum values at the angle Imax 10 a.u. I 5 a.u. 45 View vide n Malus s Law View an interesting vide: Plarized Light Explained + Experiments Exercise 2 Fur plarisers are placed n an ptical bench between an unplarised light surce and a phtcell. The plarising axes f the plarises w.r.t. the vertical are 30, 60, 45 and -30. If the incident intensity n the first plariser is 100 a.u., what is the intensity recrded by the phtcell? What angle must the last plariser by set at s that the intensity recrded by the phtcell is (i) a minimum and (ii) a maximum?
Slutin Yu need t draw a careful anntated diagram f the situatin and then apply Malus s Law t each plariser. I I cs 2 max The unplarised light in passing thrugh plariser P 1 is reduced in intensity by 50%. I 100 a.u. I 50 a.u. 0 1 Fr the linear plarised light passing thrugh P 2, the angle between the plarising axes f P 2 and P 1 is 30 I I m ax 50 a.u. 60 30 30 2 2 2 Imax cs 50 cs 30 37.5 a.u.
Fr the linear plarised light passing thrugh P 3, the angle between the plarising axes f P 3 and P 2 is 15 I I m ax 37.5 a.u. 60 45 15 2 2 3 Imax cs 37.5 cs 15 35.0 a.u. Fr the linear plarised light passing thrugh P 4, the angle between the plarising axes f P 4 and P 3 is 75 I I m ax 35 a.u. 45 30 75 2 2 4 Imax cs 35 cs 75 2.3 a.u. Hence, the intensity recrded by the phtcell is 2.3 a.u. The plariser P 3 is set at an angle f 45. If zer intensity is t be recrded by the phtcell, the angle between the plarising axes (transmissin axes) must be 90. Therefre, plariser P 4 can be set t the angle -45 since cs(90 ) = 0. 4 45 Fr a maximum (I = 2.3 a.u.), the plarisatin axes f P 3 and P 4 must be parallel. Therefre, P 4 shuld be set t 45 t give a maximum since cs(0) = 1. 4 45
Exercise 3: Cmputer Simulatin Experiment Yu can d an nline versin f Malus s experiment at http://tutr-hmewrk.cm/physics_help/plarized_light.html Recrd values f the angle and intensity t draw the graphs shwn in the slutin t Exercise 1. Why is the experimental results t gd? VISUAL PHYSICS ONLINE If yu have any feedback, cmments, suggestins r crrectins please email: Ian Cper Schl f Physics University f Sydney ian.cper@sydney.edu.au