1.8 light and matter

Prep by TEXTILE ENGINEER TANVEER AHMED

1

THE INTERACTIONS OF LIGHT WITH MATTER

Prep by TEXTILE ENGINEER TANVEER AHMED2

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.


Introduction

the white light beam, considered as a bundle of waves with wavelengths covering

the range 400–700 nm,

can also be considered as a wave-bundle in which thewaves have components which vibrate in planes mutually at right angles to one anotheralong the line of transmission.

If the wave vibrations are confined/restricted /bound/held to one plane we describe the radiation as being

plane polarised.

Polarisation effects are important when we consider reflections from glossy surfaces and mirrors.


4

Refraction of light


Snell’s lawRefraction into the interior of the film takes place according to Snell’s law,

Which states that when light travelling

through a medium of refractive index n1 encountersand enters a medium of refractive index n2 then the light beam is bent through an angle

according to Eqn 1.11:

where i is the angle of incidence and r is the angle of refraction


6

Refraction of light• 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°.


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Refraction of light

• 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).


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Surface reflection of light


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Fresnel’s law

•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.


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Fresnel’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).


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Surface reflection of light• 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).


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Surface reflection of light• 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).


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Surface reflection of light•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.


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Light scattering and diffuse reflection


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• 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.


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Light scattering and diffuse reflection• 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.


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polar reflection or gonio-photo-metric reflection 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).


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TO Assess the Gloss and Coloristic Properties• 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).


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• 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).


20Absorption of light (Beer–Lambert law)

If the paint layer contains coloured pigment particles (usually 0.1–1 mm in size) thenthe 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 properties can be treated in the same way as those of dye solutions which absorb but do not scatter light.


21

Transmission of Light through dye solutions

• 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),

2. Beer’s law (1832),


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Lambert’s or Bouguer’s law (1760)•which states that layers of equal

thickness ofthe same substance transmit the same fraction of the incident

monochromatic radiation, whatever its intensity


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Beer’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.


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The 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 * cwhere ε is the wavelength-dependent molar absorptivity coefficient with units of M-1 cm-1.


25

The 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


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The Beer-Lambert law 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 fraction of photons absorbed will be σ* N * A * dz / A so,

Integrating this equation from z = 0 to z = b gives:


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The 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


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The 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.


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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).


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•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


•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:


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The 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

1.8 light and matter

Education

light scattering

reflected light

polarised light

reflection prep

light beam incident

incident light beam

white white light

light reflectedfrom