Lecture # 8 POLARIZATION OF L IGHT

1. Lecture # 8POLARIZATION OF LIGHT

2. Plan of the lecture I. Light Polarization • Natural and polarized light • The Malus law • Bruster’s law • Double refraction • Nicole prism • Optically active substances • Saccharimetry. Polarising Microscope II. Interaction of the light with subject

3. Biological and Medical Application of polarized light • Polarimetry: an optical method of researching of biological medium with natural or induced optical activity based on the measurements of optical rotation. • This method is used to determine the optical activity of blood serum proteins for the purpose of cancer diagnosis, for determination of blood sugar in the urine and in biophysical studies as well as in the food industry. • Appropriate measuring instruments called polarimeters or saccharimeter (if they are specially adapted for measuring the concentration of sugar).

4. 2. Polarizing microscope: allows to observe optically anisotropic objects or optically active substances and structures (muscular, bone and neural tissues), which are invisible in ordinary optical microscope. 3. The investigation of photoelasticityphenomena, wherein the transparent body under the action of mechanical stresses change their optical activity and it made them visible in polarized light. Photoelasticity phenomenon is used in traumatology for determining the mechanical stress that arises in the bone and in the joints.

5. 4. Phototherapy (light or color therapy) – therapy with help of polarized lighy. Currently, it is used extensively in various fields of medicine to treat and prevent a wide range of diseases as well as rehabilitation after injuries and surgeries. It has integrated healing effect on the human body: it improves microcirculation, improves skin, strengthens the immune system, promotes wound healing and pain relief High therapeutic effectiveness of polarized light was confirmed in the treatment of children of different ages, including neonatology and geriatrics, and frequently ill patients.

6. I. Light Polarization Light is electromagnetic waves of optical range (from 10 nm to 400 µm = 400.000 nm). All electromagnetic waves conditionally according to λ (or f) are divided into several ranges formingElectromagnetic waves scale: Gamma radiation Roentgen radiation (or X-radiation) Optical radiation a) ultra-violet rays (λ = 10 - 380 nm ) b) visible rays (λ = 380 - 760 nm ) c) infra-red rays (λ =760 – 400.000 nm) 4. Radio-waves (or Hertz(ian) waves).

7. Visible range of optical radiation is rays perceived by human eye; • λ from 380 nm (0,38 µm) to 760 nm (0,76 µm) – from violet colortored color.

8. An electromagnetic wave is the propagation of an alternating electromagnetic field (EMF). Two basic characteristics of EMF: • vector E - electric field intensity (V/m) • vector B - magnetic induction (Tl). • Electromagnetic wave is a transverse wave, because the direction of oscillations of E-vector and of B-vector being perpendicular to each other, and to the direction of wave propagation (v – velocity vector): E ┴ B ┴ v

9. Electromagnetictransverse wave

10. If oscillation of E-vectoroccursin one plane along one line, the light is called polarized(or plane-polarized or totally polarized)light. Individual (isolated) atom emits polarized light. Ē

11. Light in which direction of E-vector changes chaotically with different amplitudes is called natural light(or non-polarized light). • The light wave emitted by a body as a whole, is formed by addition of waves emitted by a multitude of atoms with different orientation of E-vector, chaotically changing in time. • All natural sources of light (sun, flame of candle, lamp) emit non-polarized light. Natural light

12. Partially polarized light : direction of E-vector changes chaotically, but the amplitudes of oscillation in some directions notably differ from that in other directions. Partially polarized light.

13. Directions of oscillations of E-vector in the plane ( ): Natural Plane-polarized Partially polarized lightlight light

14. Natural light (a), plane-polarized light (b), partially polarizedlight (c) a - circle b - segment c - ellipse

15. Conventionally the ray of light can be shown as a straight linewith different number of dots and dashes; • their ratio reflects a degree of polarization. a c b d Indication: natural (a), plane-polarized (b, c), partially polarizedlight (d)

16. Light polarization - is a process of transformation (conversion) of natural light into polarized or partially polarized light. Methods of obtaining of polarized light: • Polarizers • Light polarization on the boundary of two transparent dielectrics • Light polarization in optically anisotropic media (under double refraction) Polarizers are devices that extract polarized light from natural light.

17. 1) In is intensity of natural light incident on a polarizer, Ip is intensity of polarized light exited the polarizer

18. 2)Analyzer is a second polarizer which rotates polarization plane of polarized light. Malus law: • I is the intensity of plane-polarized light exited the analyzer; • I0 is the intensity of l plane-polarized light exited the first polarizer and incident on the analyzer; • φ is the angle between the principal planes of polarizer and of analyzer. If φ = 0, I = I0 ; if φ = 90º,I= 0.

19. 3) In the general case incidence of natural light on the interface of two transparent dielectrics forms 2 rays -reflected and refracted (both of rays are partially polarized)

20. the reflected ray is completely polarized, the refracted ray is partially polarized, though the degree of its polarization at this is maximum. n is the relative index of refraction of the second medium to the first one; • iBis calledBrewster's angle. • Brewster's law : if the angle of incidence (αB) meets condition

21. Stoletov’s packet is a set of thin transparent plates; is used to make the refracted raycompletely polarized as well. • The degree of light polarization for the refracted ray increases on every interface of plates, due to which the light exited the packet is almost completely polarized. αB

22. 4) Double refraction (orbirefringence): phenomenon of splitting a light beam as it passes through the opticallyanisotropic media due to the dependence of refractive index on its polarization and direction of propagation. Anisotropic mediaaremedia whose optical characteristics depend on the direction of light propagation therein (for example, crystals of Iceland spar). Optical axis of the crystal is a direction in which the velocity of light propagation is ultimate (i.e. either maximum, or minimum); in this direction double refraction is not observed.

23. O׳ • If a natural light ray is incident on an optically anisotropic crystal, two rays are formed due to double refraction: o e O • ordinary ray(o) - propagates in the plane of ray incidence, satisfies the law of light refraction; • extraordinary ray(e), propagates in the principal optical plane (plane formed by the incident ray and the crystal optical axis, which passes through the point of ray incidence). • Both rays arecompletely polarized: e-ray is polarized in the principal plane, o-ray is polarized in a plane perpendicular to the principal one.

24. The propagation velocities (v) of the ordinary and extraordinary rays in an optically anisotropic medium are different. Hence, the indices of refraction of the medium are different for these rays. • Positive crystals:vo > ve • Negative crystal: vo < ve vo - the propagation velocity of the o-ray, ve - the propagation velocity of the e-ray

25. Dichroism is a phenomenon at which one of the rays (o-ray or e-ray) is absorbed more than other (observed in some crystals with double refraction - tourmaline, herapathite). • As a result, only one completely polarized ray exits there from (at sufficient thickness of a crystal possessing dichroism property). • Such crystals can be used as a light polarizers in optics.

26. 4) Nicol prism(or nicol) consists of two parts (made of Iceland spar) bonded with Canadian balsam • is used to obtain achromatic polarized light, • Index of refraction: for Canadian balsam (n = 1.55), for e-ray in Iceland spar (ne = 1.49), for o-ray inIceland spar (no = 1.66) ne< n < no

27. The prism is designed so that (the angle of incidence of the o-ray on the interface of Iceland spar and Canadian balsam is greater than the angle of total internal reflection) • only e-ray passes through the prism and exits there from totally polarized, • o-ray is totally reflected at the Iceland spar and Canadian balsam interface and is absorbed by the blackened side face of the prism. Canadian balsam Natural light

28. Optically Active Substancesare substances, which are able to rotate the plane of light polarization of polarized light. • αis an angle of rotation, • l is a length of the path passed by the light in the optically active substance, • α0 is rotation constant (depends on the temperature and the light wavelength) Optically Active Substances α l • Rotation dispersion : dependence of the angle of rotation of the polarization plane on the light wavelength.

29. For solutions of optically active substances in inert solvents (for example, solutions of sugar in water) the angle of rotation (α) of the light polarization plane depends on the concentration (c) of the optically active substance - Biot law: • [α0] is specific rotation, depends on the wavelength, the solution temperature, and the properties of the solvent. [α0] ~ 1 / λ2

30. As evident, one can determine the concentrations of an optically active substance in the solution by this formula. This method of study is called polarimetry or saccharimetry. The respective instruments are called polarimeters or saccharimeters.

31. Polarizing Microscope • The operation of a polarizing microscope is based on light polarization. A polarizing microscope differs from an ordinary optical one in that it contains a polarizer and analyzer. • The polarizer is placed before the condenser and polarizes the light that illuminates the object studied. The analyzer is in the microscope drawtube. • Polarizing microscope allows to observe optically anisotropic objects or optically active substances only. • If we have an isotropic sample devoid of optical activity, and the principal planes of the polarizer and analyzer are mutually perpendicular, the field of vision in the polarizing microscope will be dark.

32. Tissues of living organisms contain various right-handed and left-handed substances, the total optical activity of biologic tissues being practically equal to zero. Sothe polarizing microscope is only used for studying structures possessing optical anisotropy. (muscular, bone and neural tissues). Polarization images of the muscular (myocardium) (a), (b) and the large intestine wall (c), (d) tissue histological sections.

33. II. Interaction of the light with subject1. Light absorption • Light absorption is decrease in intensity of light as it passes through a substance due to conversion of light energy into other kinds of energy. • The absorption of light in a substance is described by Bouguer's law: whereIis an intensity of light past through the layer of absorbing substance with thickness l;I0is an intensity of incident light, and kλ is the monochromatic natural absorption coefficient. • The monochromatic natural absorption coefficientis a characteristic of the absorbing medium that depends on light wavelength.

34. Of practical importance is the case when a substance dissolved in a solvent absorbs light, and light absorption by the solvent can be neglected. In this case, the intensity of light that has passed through the solution depends on the concentration of the solute. • This dependence for diluted (not too concentrated) solutions has the form where с - is the molar concentration of the solution, and א λ is the monochromatic natural molar absorption coefficient. This formula is often called the Bouguer-Lambert-Beer law.

35. It is often written in the form where א 'λis the monochromatic molar absorption coefficient. It is obvious that א 'λ = א λ·lge ≈0.43·א λ As characteristics of light absorption by a substance, the following values can also be used: light-transmission factor (τ) and optical densityof the solution (D). Hence, the Bouguer-Lambert-Beer law can be written in the form

36. The optical density of the solution, similar to the absorption coefficients, depends on the light wavelength. The dependences of absorption coefficients of a substance, or the optical density of a substance solution, on the light wavelength are called the absorption spectra of this substance. • Determination of the optical density is the basis of concentration colorimetry – a photometric method of substances concentration determination in painted solutions.

37. 2. Light Scattering • Light scatteringis a process involving a change in the direction of propagation of a fraction of the light as it passes through a substance. The cause of light scattering during its propagation in a medium is the presence of optical heterogeneities, i.e. areas in the medium, which have different index of refraction values. • There are two kinds of light scattering, viz. scattering in a turbid mediaand molecular scattering.

38. TheTyndall effect • Scattering in a turbid media is scattering on minute foreign particles in a homogeneous transparent substance (for example, smoke, mist and others). Scattering in a turbid media is also called theTyndall effect. • Molecular scattering is the result of continuously emerging and disappearing areas whose density is greater or less than the average substance density. These areas are formed in transparent media due to the chaotic motion of its constituent particles. Light source Light source Screen Colloid solution Screen Transparent solution Vibrating electron Nuclei Incident light Scattering light

39. where m is the scattering coefficient(more precisely, the natural scattering coefficient). • The light scattering coefficient depends on the wavelength, viz. the less the wavelength the greater the light scattering. As a result, during scattering of white light, blue, dark blue and violet rays will scatter most; and red and orange rays will pass best without scattering. That is why the sky is blue at daytime, and the sun is red at sunset. • Light scattering is described by a formula similar to Bouguer's law:

40. The technique of determining indices, which characterize light scattering, is called nephelometry, and the measurement instruments used therefore are called nephelometers.