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Two models for the description of light

Two models for the description of light. The corpuscular theory of light stating that light can be regarded as a stream of particles of discrete energy called photons . Their energy E is defined by: E = h n.

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Two models for the description of light

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  1. Two models for the description of light The corpuscular theory of light stating that light can be regarded as a stream of particles of discrete energy called photons. Their energy E is defined by: E = hn The description of most atomic processes such as absorption, fluorescence, and the photo-electric effect require the photon approach. The wave theory of light stating that light can be treated as a wave with an electrical and magnetic field, each described by a vector. The magnitude of the electric field vector Y at position x and time t and the amplitude ao (constant) is given by: Y = aosin[(2p/l)(x+vt)] The velocity (v) is related to the frequency (n) by the equation: v = ln The electro-magnetic wave intensity(I) is proportional to the square of the amplitude: I = K(ao)2 K is a constant of proportionality and depends upon the properties of the medium containing the wave.

  2. Polarisation of Light linearly polarized circularly polarized

  3. Four principal interactions of light with matter Ignoring fluorescence, the interactions of light with matter can be expressed thus: Io = Ireflected + Iscattered + Iabsorbed + Itransmitted transparentmaterial translucentmaterial

  4. Refractive Index and Polarizability of Matter

  5. Refraction and the refractive index When light enters a transparent medium of different refractive index, n, it is refracted (Snell’s Law): n = sinq1 / sinq2(angles of incident & refraction, respectively) sinq1 / sinq2 = n2 / n1 The velocity of a light wave changes when light enters a transparent medium of different refractive index but not thefrequency: velocity = nl; n = c / v = lvac / lsubs Graphical change of wavelength with change of n.

  6. Total Internal Reflection At the critical angle qc, the emerging ray travels exactly along the surface. Exceeding this angle results in total reflection (no light is lost). The critical angle is given by: sin qc = n(low) / n(high)

  7. Dispersion and Colour The refractive index of a transparent solid varies with wavelength.This is called dispersion.

  8. Polarisation by Reflection The reflectivity or reflectance of a surface is given by:Rs = [sin(q1 – q3) / sin (q1 + q3)]2 Rp = [tan(q1 – q3) / tan (q1 + q3)]2 The Brewster’s angle

  9. Birefringence of Optically Anisotropic Matter Birefringence A nematic phase, for example, is essentially a one-dimensionally ordered elastic fluid in which the molecules are orientationally ordered along the director. The nematic phase is birefringent due to the anisotropic nature of its physical properties. Thus, a light beam entering into a bulk nematic phase will be split into two rays, an ordinary ray and an extraordinary ray(along the director). These two rays will be deflected at different angles and travel at different velocities through the mesophase, depending on the principal refractive indices. If the extraordinary ray travels at a slower velocity than the ordinary ray, the phase has a positive birefringence. We can write for most optically uniaxial calamitic mesophases:ne > no with Dn = ne-no

  10. Double Refraction and Birefringence of an Anisotropic Transparent Medium q The relationship between the magnitude of n’e and the angle q that the ray makes with the optic axis is: 1 / (n’e)2 = cos2q / no2 + sin2q / ne2 Snell’s Law: sinq1 / sinq2 = n2 / n1

  11. Birefringence and the Indicatrix

  12. Molecular Theory of Refractive Indices Lorentz local field for an isotropic medium: Eloc= [(e+ 2) / 3] Eeis the mean permittivity Using e = n2derived from the Maxwell’s Equations, the Lorenz-Lorentz expression relates the refractive index to the mean molecular polarizability: n2 – 1 / n2 + 2 = Na / 3e0 whereN is the number density (d NA / M ), a the mean polarizability, and e0 = 8.86 10-12 As/Vm Anisotropic Molecular Polarizability ne2 – 1 / n2 + 2 = Na / 3e0 no2 – 1 / n2 + 2 = Na / 3e0 with n2 = 1/3 (ne2 + 2no2)

  13. Defect Textures in Thermotropic Liquid Crystals Schlieren Texture of a Nematic Phase

  14. Textures of a SmA Phase

  15. Textures of a SmC Phase broken focal-conic schlieren

  16. Textures of a Colh Phase

  17. Mosaic Texture of a SmB Phase

  18. Deformations in Thermotropic Liquid Crystals Since the nematic phase can be treated as an elastic continuum fluid, three possible elastic deformations of its structure are possible: The splay deformation, the twist deformation, and the bend deformation. The elastic constants associated with them are k11, k22, and k33, respectively.

  19. Natural textures exhibited by calamitic LCs(as seen between crossed polarizers)

  20. Paramorphotic textures associated with calamitic LCs(as seen between crossed polarizers)

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