nd ear laborator script L Light Scattering Department o Phsics and Astronom nd Year Laborator L Light Scattering Scientiic aims and objectives To determine the densit o nano-spheres o polstrene suspended in the tubes o water b their Raleigh scattering cross section. To determine the validit o the hpothesis that the scattering mechanism is Raleigh and not geometric or Mie. Learning Outcomes To determine the origin o sstematic errors To determine the validit o using web based literature to ind values or material properties. To know that there are dierent regimes or light scattering depending on the size o an object Apparatus Four light scattering stations with dierent laser wavelengths o 473 ± 5 nm o 635 ± 5 nm o 660 ± 5 nm o 780 ± 15 nm Each station is comprised o o Laser o Moving light detector, ampliier and meter o Ruler Saet instructions This eperiment uses low power class IIIb laser beams, one o which is invisible. Never look directl into the beam, Take care not to allow shin objects jeweller, watches etc to relect the beam at ee level. Be particularl careul with the invisible laser. χ Ecel sotware September 010 V.1 Page 1
nd ear laborator script L Light Scattering Task 1 - Pre-session questions You are required to complete the questions ound at the back o the script beore starting our laborator work. These questions will prepare ou or the eperiment b teaching ou about dierent scattering mechanisms. Task The eperiment The objective is to determine the number densit o polstrene spheres suspended in tubes o water b measuring the change in intensit o scattered light rom laser beams o varing wavelength. The dependence o scattering attenuation on laser wavelength should ollow that o Raleigh scattering since the polstrene sphere size 11 nm is less than the wavelength o light. However, ou should check this hpothesis in an attempt to eclude other possible scattering mechanisms such as Mie scattering or geometric scattering. The attenuation o laser light in the tube has contributions rom the absorption o water itsel α and rom the scattering rom the polstrene spheres Nσ. You should account or both in our attempts to validate the Raleigh equation and quanti the densit o spheres in the tubes. This eperiment is particularl prone to sstematic errors. For eample, misalignment o the laser such that the beam is not travelling down the centre o the tube, or misalignment o the detector such that it becomes urther awa rom the tube as the distance rom the laser source increases. You should make some measurements and calculations to numericall quanti these kinds o contributions to the error in the eperiment and determine whether the are signiicant or not. These assessments o sstematic errors should be combined with repeat measurements to determine random error contribution. χ should be used when itting straight lines to our data. Task 3 Reporting You should report a number densit o the polstrene spheres and a proportion o the volume o the tubes that is taken up b the spheres. You should assess whether the hpothesis that Raleigh scattering is the dominant mechanism is correct based on our eperimental evidence. You should also spend time considering both sstematic and random errors that could occur in the eperiment and report our indings. September 010 V.1 Page
nd ear laborator script L Light Scattering Appendi o supporting inormation Contents 1. Scattering o light. Mie, Raleigh and geometric scattering 3. Measurement procedure 4. Absorption coeicient o water 5. Straight line itting using χ 6. Compound errors 7. Sstematic errors 1. Scattering o light I a light beam passes through a medium in which there are suspended spheres with a reractive inde that is dierent rom that o the medium, the beam is attenuated because some o the light is scattered out o the original beam direction. This is obvious in ogg weather and when sunlight passes through a dust atmosphere. Scattering o light is important in astronom, where light rom stars is oten viewed through interstellar dust clouds, and also in the optical ibre telecommunications industr, where light scatters rom impurities and inhomogeneities in the ibre. The scattering is convenientl described in terms o the scattering cross-section σ o the sphere concerned; this is the eective area which the sphere eliminates rom the beam. I we consider a beam o intensit I and area A propagating through a suspension o spheres with N spheres per unit volume, each o which has a scattering cross-section σ. The decrease in intensit di on passing through a distance d is given b: di total area o scatterers - raction o beam intercepted A1 I area o beam Thereore: Nvolume o liquid σ N Ad σ Nσd A A A I ln I Nσ I I ep Nσ l n 0 or 0. A3 The light intensit will also deca as a consequence o absorption b the water molecules. This is characterised b the absorption coeicient α. The attenuation processes act independentl o each other and so their separate contributions can be added together. The variation o the intensit with is thereore given b: I I ep[ Nσ α ] A4 0 Together with eperimental data or the deca o the intensit o light, equation A4 can be used to determine Nσ α or the dierent wavelengths o laser b itting a straight line to a ln I vs plot. September 010 V.1 Page 3
nd ear laborator script L Light Scattering. Mie, Raleigh and geometric scattering The scattering o electromagnetic radiation b spherical particles can be analsed rigorousl b solving Mawell s equations or the sstem. Such an analsis is normall done with the aid o computers and can accuratel predict man scattering phenomena. Gustav Mie was the irst scientist to attempt these calculations and hence the generic terminolog or scattering where the light has comparable wavelength to the size o the sphere is know as Mie scattering. Although the Mie scattering approach is valid or spheres o an size, there are two limiting cases that ield simple analtical epressions or σ. Raleigh Scattering applies when a << λ, where a is the radius o the sphere and λ is the wavelength o light. The scattering cross-section or Raleigh scattering is where n n n 1 5 18π a σ 4 3λ 6 n n 1. n 1 is the reractive inde o the sphere and n that o the medium. A5 Geometric Scattering applies when a >> λ. The sphere simpl blanks out the light rom its geometrical shadow and σ πa. In this eperiment we hpothesise that scattering should ollow the Raleigh equation A5 since the polstrene sphere diameter o 11 nm is signiicantl smaller that o the shortest laser wavelength. Using our eperimental results ou should discuss the validit o this hpothesis. One approach is to plot our eperimentall determined values or σ against 1/λ 4 and assess the linearit o the plot. Raleigh scattering should eild a perectl straight line. The reractive inde o water varies rom 1.345 at 400 nm to 1.330 at 800 nm The reractive inde o polstrene varies rom 1.587 at 400 nm to 1.578 at 800 nm 3. Measurement procedure For each set o apparatus, the relative intensit o the beam as a unction o distance along the tube should be measured. Since the measurements o scattered intensit as a unction o distance need to be made with minimal background light, it is a requirement that the lid on the bo be closed. Thereore the number o turns made b the screw thread needs to be calibrated against distance beore measurements can proceed. A second requirement is to setup the detector so it measures the intensit o the scattered light with the greatest dnamic range, to give the greatest sensitivit to the measurements. You should set the gain controls o the photodiode ampliier to achieve this condition. Finall ou will need to zero the photodetector ampliier so that ou are onl measuring the scattered light rom the laser as it passes through the tube, and not stra light rom the room lights or windows. This can be done b blocking the laser with a piece o black card or similar, closing the lid, and then setting the ampliier controls so that the signal reads zero. Do not zero the detector b turning the laser September 010 V.1 Page 4
nd ear laborator script L Light Scattering o since lasers need a considerable length o time to settle to a stable emission power. 4. Absorption coeicient o water Water is highl transparent in the visible part o the spectrum since there are no resonant electronic or vibrational transitions. However a small background absorption is present and has been characterised and documented man times. Data or the absorption coeicient o pure water taken rom an online resource http://omlc.ogi.edu/spectra/water/abs/ has been plotted below. You should consider the validit o the use o this data in our eperiment, and using this data, or other data that ou can ind, determine values and associated errors or the absorption coeicients required at the dierent laser wavelengths. 5. Straight line itting using χ The χ ecel spreadsheet has been developed to enable ou to perorm a χ it to our data that takes into account our error bars. In general the error bars should be larger than our error bars and hence dominant. I this is not the case rearrange our data appropriatel. I our data are not epected to be represented b a straight line e.g. b an eponential unction o then tr to transorm our values appropriatel. Then ollow these instructions. 1. Cop and paste our, and σ values into Columns C, D and E respectivel, starting at Row 17. Remember to use Paste Special i our values are derived rom ormulae.. Enter the number 1 in Column B or ever Row in which ou have data. September 010 V.1 Page 5
nd ear laborator script L Light Scattering September 010 V.1 Page 6 3. Read o the values or the gradient and uncertaint and intercept and uncertaint rom cells B5, C5, B6 and C6. 4. The goodness o it how accuratel our straight line model actuall represents the data can be estimated rom the χ value Cell B8 divided b the number o data given in Cell B9. For a good it the χ /n value should be approimatel 1.0. A value signiicantl less than this shows ou have iddled our data, or over-estimated the uncertainties on our points! A value signiicantl greater than 1.0 shows that the data are not well-represented b the model think about wh this might be. 5. Don t orget to plot the itted line using mc in our graph as a line alongside our data-points with error bars. Do not use Add Trendline. I everthing has worked correctl, χ /n ~ 1.0, and errors are Gaussian, then approimatel 68% o the points should lie on the itted line within their error bars. 6. Compound errors Absolute error Proportional error n n n 1 n / 4 7. Sstematic errors See http://en.wikipedia.org/wiki/sstematic_error and reerences therein.
nd ear laborator script L Light Scattering Pre-lab multiple choice questions Mie scattering can onl be calculated numericall or a speciic sstem o scattering particles. Using an online numerical calculator ound at http://omlc.ogi.edu/calc/mie_calc.html ou can investigate Mie scattering, and see how the scattering direction and cross section depends on particle size. Using the sotware ind out which is the most likel particle size or the angular scattering patterns below. You can assume polstrene spheres as in the eperiment. Q1 A: 0.05 µm B: 0.1 µm C: 0.5 µm D:.0 µm Q A: 0.05 µm B: 0.1 µm C: 0.5 µm D:.0 µm Q3 A: 0.05 µm B: 0.1 µm C: 0.5 µm D:.0 µm September 010 V.1 Page 7