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# 1.8 light and matter

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### 1.8 light and matter

1. 1. 1 Prep by TEXTILEENGINEER TANVEER AHMED
2. 2. Introduction• Consider a beam of white light incident on the surface• of a coloured paint film.• As soon as the light meets the paint surface  the beam undergoes refraction,  and some of the light is reflected.• The refracted beam entering the paint layer then undergoes  absorption  and scattering,  and it is the combination of these two processes  which gives rise to the underlying colour of the paint layer.• In order to have some appreciation of the optical factors which give the surface overall appearance (including colour and gloss or texture)• we need to outline the laws  that affect the interactions of the light beam with the surface. Prep by TEXTILE ENGINEER TANVEER AHMED 2
3. 3. Introductionthe white light beam, considered as a bundle of waves withwavelengths covering the range 400–700 nm,can also be considered as a wave-bundle in which the waves have components which vibrate in planes mutually at right angles to one another along the line of transmission.If the wave vibrations are confined/restricted /bound/held toone plane we describe the radiation as being plane polarised.Polarisation effects are important when we consider reflections from glossy surfaces and mirrors. Prep by TEXTILE ENGINEER TANVEER AHMED 3
4. 4. 4Refraction of light Prep by TEXTILE ENGINEER TANVEER AHMED
5. 5. Snell’s lawRefraction into the interior of the film takes place according toSnell’s law,Which states thatwhen light travelling through a medium of refractive index n1 encounters and enters a medium of refractive index n2 then the light beam is bent through an angleaccording to Eqn 1.11: where i is the angle of incidence and r is the angle of refraction Prep by TEXTILE ENGINEER TANVEER AHMED 5
6. 6. 6 Prep by TEXTILE ENGINEER TANVEERRefraction of light AHMED • A typical paint resin has a refractive index similar to that of ordinary glass (n = 1.5) • and so a beam of radiation incident on the surface at 45° • will be bent towards the normal by 17° • to a refraction angle of approximately 28°.
7. 7. 7 Prep by TEXTILERefraction of light ENGINEER TANVEER AHMED • The refraction angle depends on  the wavelength; • the ability of glass to refract blue radiation more than red radiation is apparent in the production of a visible spectrum when  white light is passed through a glass prism. • Refractive indices are therefore normally measured using  radiation of a standard wavelength  – in practice, sodium D line radiation (yellow-orange light of wavelength 589.3 nm).
8. 8. 8Surface reflection of light Prep by TEXTILE ENGINEER TANVEER AHMED
9. 9. 9Fresnel’s law Prep by TEXTILE ENGINEER TANVEER AHMED • A light beam incident normally (vertically) on a surface or any boundary • between two phases of differing refractive index will suffer partial back- reflection according to • Fresnel’s law (Eqn 1.12): where r is the reflection factor for un- polarised light and n is n2/n1.
10. 10. 10 Prep by TEXTILE ENGINEER TANVEER AHMEDFresnel’s law• If the incident light beam is white then  the light reflected from the surface will also be white  (white light needs to undergo selective absorption before it appears coloured).• This small percentage of white light reflected from the surface affects  the visually perceived colour,• and instrumentally measured reflectance values should indicate whether the specular reflection is  included (SPIN) or  excluded (SPEX).
11. 11. 11 Prep by TEXTILE ENGINEER TANVEERSurface reflection of light AHMED• For the air (n = 1) and• resin layer (n = 1.5) interface the total surface reflection at ▫ normal angles is about 4% (r = 0.04).• At angles away from the normal, however, this  surface or specular (mirror-like) reflection varies• depending on  the polarisation of the beam relative to the surface plane (Figure 1.23).
12. 12. 12 Prep by TEXTILE Surface reflection of light ENGINEER TANVEER AHMED• The curves in this diagram show that• the reflection of the perpendicularly polarised component becomes  zero at a certain angle (the Brewster angle),• and the reflected light at this angle is polarised  in the one direction.• The reflection of both polarised components becomes  equal at normal incidence (0°),• and again at the grazing angle (90°), at which point the surface reflects  virtually 100% of the incident light (surfaces always look glossy at high or grazing angles).
13. 13. 13 Prep by TEXTILE Surface reflection of light ENGINEER TANVEER AHMED• Thus light reflected from most surfaces is  partially polarised.• This is why Polaroid glasses are useful for  cutting out glare from wet roads  when driving,  and for seeing under  the surface of water on a bright day.
14. 14. Light scattering and diffuse 14reflection Prep by TEXTILE ENGINEER TANVEER AHMED
15. 15. 15 Prep by TEXTILELight scattering and diffuse ENGINEER TANVEER AHMEDreflection • Part of the light beam is not specularly reflected at the surface but  undergoes refraction into the paint layer. • This light will encounter pigment particles, which will  scatter it in all directions. • The extent of this scattering will depend on  the particle size  and on the refractive index difference between the pigment particles  and the medium in which  they are dispersed, again according to Fresnel’s laws.
16. 16. 16 Prep by TEXTILE ENGINEER TANVEER AHMEDLight scattering and diffusereflection• With white pigments like• titanium dioxide (n > 2) the scattering will be  independent of wavelength,  and most of the incident light will be scattered in random directions.• A high proportion will reappear at the surface and give rise to the diffuse reflected component;  with a good matt white the diffuse reflection can approach 90% of the incident light.• White textile fibres and fabrics produce a high proportion of diffusely reflected light, either because of the scattering at the  numerous interfaces in the microfibrillar structure of natural fibres like cotton, wool and silk or,• in the case of synthetic fibres, from the presence of titanium  dioxide pigment in the fibres.
17. 17. 17 Prep by TEXTILEpolar reflection or gonio-photo-metric ENGINEER TANVEER AHMEDreflection curve In practice there will be a balance between specular and diffuse reflected light • which can be described by the polar reflection or gonio-photo-metric reflection curve • Shown in Figure 1.24).
18. 18. 18 Prep by TEXTILETO Assess the Gloss and Coloristic ENGINEER TANVEER AHMEDProperties• To assess the gloss, determined by the proportion of the  Specular component,• the sample should be viewed at  an angle equal to the incident, i.e. at 60°• for the case illustrated in Figure 1.25.• The extent of the diffuse component• (and any colour contribution) is then assessed by  viewing at right angles to the surface (that is,  at an incident angle of 0°,• Figure 1.26).
19. 19. 19Light scattering and diffuse Prep by TEXTILE ENGINEER TANVEER AHMEDreflection• Thus the direction of reflected light plays a large part in the  appearance of a surface coating.• If it is concentrated within a narrow region at an angle equal to the angle of incidence  the surface will appear glossy, i.e. it will have a high specular reflection.• Conversely if it is reflected indiscriminately/ random /jumbled / multifarious at all angles it will have  a high diffuse reflection and will appear matt.• Gloss is usually assessed instrumentally at high angles• (60 or 85°)• as the specular component is more important at such high angles ▫ (even a ‘matt’ paint surface shows some gloss at high or grazing angles).
20. 20. Absorption of light 20 (Beer–Lambert law)If the paint layer contains coloured pigment particles Prep by TEXTILE (usually 0.1–1 mm in size) then ENGINEER TANVEER AHMEDthe light beam travelling through the medium will be partly absorbed and partly scattered(Figure 1.1).Some particles are so small (< 0.2 mm) that they can be consideredto be effectively in solution, and their light-absorption propertiescan be treated in the same wayas those of dye solutions which absorb but do not scatter light.
21. 21. 21 Prep by TEXTILETransmission of Light through dye ENGINEER TANVEER AHMEDsolutions • The transmission of light of a single wavelength (monochromatic radiation) through dye solutions or dispersions of very small particles • is governed by two laws: 1. Lambert’s or Bouguer’s law (1760), 1. Beer’s law (1832),
22. 22. 22 Prep by TEXTILE ENGINEER TANVEER AHMEDLambert’s or Bouguer’s law (1760)• which states that layers of equal thickness of the same substance  transmit the same fraction of the incident monochromatic radiation, whatever its intensity
23. 23. 23 Prep by TEXTILE ENGINEER TANVEER AHMEDBeer’s law (1832)• which states that the absorption of light is proportional to the number of absorbing entities (molecules) in its path;• that is, for a given path length, the proportion of light transmitted decreases with the concentration of the light-absorbing solute.
24. 24. 24 Prep by TEXTILE ENGINEER TANVEER AHMEDThe Beer-Lambert law• A = a(λ) * b * c  where A is the measured absorbance,  a(λ) is a wavelength-dependent absorptivity coefficient,  b is the path length,  and c is the analyte concentration.• When working in concentration units of molarity, the Beer- Lambert law is written as: A= ε *b*c where ε is the wavelength- dependent molar absorptivity coefficient with units of M-1 cm-1.
25. 25. 25 Prep by TEXTILE ENGINEER TANVEER AHMEDThe Beer-Lambert law• The Beer-Lambert law can be derived from an approximation for  the absorption coefficient  for a molecule  by approximating the molecule  by an opaque disk• whose cross-sectional area,σ , represents the effective area seen by  a photon of frequency w.• If the frequency of the light is far from resonance,  the area is approximately 0,• and if w is close to resonance  the area is a maximum.• Taking an infinitesimal slab, dz, of sample
26. 26. 26 Prep by TEXTILEThe Beer-Lambert law ENGINEER TANVEER AHMED Io is the intensity entering the sample at z=0, Iz is the intensity entering the infinitesimal slab at z, dI is the intensity absorbed in the slab, and I is the intensity of light leaving the sample. Then, the total opaque area on the slab due to the absorbers is σ * N * A * dz. Then, the Integrating this equation from z = 0 fraction of photons absorbed to z = b gives: will be σ* N * A * dz / A so,
27. 27. 27 Prep by TEXTILE ENGINEER TANVEER AHMEDThe Beer-Lambert law• Since N (molecules/cm3) * (1 mole / 6.023x1023 molecules) * 1000 cm3 / liter = c (moles/liter)• and 2.303 * log(x) = ln(x), then
28. 28. 28 Prep by TEXTILEENGINEER TANVEER AHMED
29. 29. 29 Prep by TEXTILE ENGINEER TANVEER AHMEDThe Beer-Lambert law• Suppose that we were to measure the absorption of green light by a purple dye solution• contained in a spectrophotometer cell (cuvette) of total path length 1 cm,• And that the solution absorbed 50% of the incident radiation over the first 0.2 cm;• then the• light transmittance through the cell would vary as shown in Table 1.5.
30. 30. 30 Prep by TEXTILE ENGINEER TANVEER AHMED The Beer-Lambert law• Each 0.2 cm layer of solution decreases the light intensity• by 50%,• as required by the Lambert– Bouguer law.• The quantity log (1/T), known as the absorbance,• increases linearly with• thickness or path length,• whilst the intensity decreases exponentially (Figure 1.27).
31. 31. 31 Prep by TEXTILE ENGINEER TANVEER AHMEDThe Beer-Lambert law• A plot of Beer’s law behaviour at fixed path length would show a similar linear dependence• of absorbance A with concentration. In fact the combined Beer–Lambert• law is often written as Eqn 1.18:
32. 32. 32 Prep by TEXTILE ENGINEER TANVEER AHMEDThe Beer-Lambert law• where the proportionality constant ε is known as the absorptivity; if the concentration• is in units of moles per unit volume (litre), it is known as the molar absorptivity.• The combined Beer–Lambert law can alternatively be written as Eqn 1.19:
33. 33. 33 Prep by TEXTILE ENGINEER TANVEER AHMEDThe Beer-Lambert law• Measurements of absorbance are widely used, through  the application of the Beer–Lambert law,  for determining the amount of coloured materials in solution,  including measurements of the strengths of dyes .• In practice deviations from these laws can arise from both ▫ instrumental ▫ and solution (chemical) factors,• but discussion  of these deviations is outside the scope of the present treatment