Download Adding and Subtracting in Math Club (Math in Our World) by Amy Rauen PDF

By Amy Rauen

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Example text

In such a case, N is a constant and independent of z but its form is not immediately evident for a complex material. 44) is a set of linear differential equations for the components of J (z) that can be solved directly, subject to the boundary condition: This boundary condition reflects the fact that the Jones vector will by unchanged by passage through an element of zero thickness. 7 is used. In this figure, the matrix N associated with the optical element is composed of a series of lamellae, each one of which introduces a specific optical effect.

The intensity of light observed at 0 = n/2, therefore, will be zero for a dipole oriented along this direction. 2 Scattering by a dipole. 2. 2 55 The Polarizability Tensor At optical frequencies, it is the dipole induced by the incident electric field that is normally important. The induced dipole is calculated from the following empirical relationship: [9] where a is the polarizability tensor. The induced dipole, therefore, is a measure of how facile the electron distribution is to distortion by an electric field.

Incident light with its polarization vector oriented at an angle 0 relative to the principal axes of n' has an elecT trie vector AO = A0 (cos0, sin0) . 15) with 8' = n, the incident electric vector will be transformed to Therefore, the exiting light is still linearly polarized but is rotated by an amount 20 from its original orientation. 5. 5 The rotation of linearly polarized light using a half-wave plate. 3 Anisotropic Attenuators: Dichroism A material with an anisotropic, imaginary refractive index: Jones Matrices for Simple Polarizing Elements 29 has a Jones matrix of the form: for light propagating along the z axis.

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