Introduction to Electrodynamics
4th Edition
ISBN: 9781108420419
Author: David J. Griffiths
Publisher: Cambridge University Press
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Salt absorbs in the infrared. The complex dielectric constant at wavelength 60µm is
-16.8 + i91.4. Calculate the absorption coefficient and the reflectivity at normal
incidence at stated wavelength, knowing that
5.
E = Er + iɛ¡
ɛ = n?
n = n, + in;
2wnį
a =
1
|n
R =
In + 1
where e is the dielectric constant, n is the refractive index, a is the absorption
coefficient and R is the reflectivity.
2.
=
A planar dielectric waveguide with the core refractive index n₁ 1.56 and the
1.47 is used to transmit light of wavelength o 750 nm. Suppose
cladding index n₂
=
=
the width of the waveguide is d = 1.0 μm:
(a) Determine the critical angle 0c at the interface.
(b) Calculate and plot the phase change on reflection o, as a function of angle of
incidence in the range 0c < 0
The plane z = 0 separates two media: glass(nglass = 1.51 for z < 0) and water (nH20 = 1.33 for z > 0). The optical beam of a helium-cadmium (He-Cd) laser has a wavelength in vacuum of 325 nm. Consider that the laser beam propagates in the x-z plane from the glass side towards the glass/water interface at an angle of incidence of 30° (angle between the incident beam and the normal to the interface). Determine the Cartesian components of the k-vector (kx, ky, kz) for the incident reflected, and transmitted beams.
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- The coordinates of the four I atoms in the unit cell of KIO4 are (0,0,0), (0,1/2,1/2), (1/2,1/2,1/2), (1/2,0, 3/4). By calculating the phase of the I reflection in the structure factor, show that the I atoms contribute no net intensity to the (114) reflection.arrow_forwardA colloid consists of particles of one type of substance dispersed in another substance. Suspensions of electrically charged microspheres (microscopic spheres, such as polystyrene) in a liquid such as water can form a colloidal crystal when the microspheres arrange themselves in a regular repeating pattern under the influence of the electrostatic force. Colloidal crystals can selectively manipulate different wavelengths of visible light. Just as we can study crystalline solids by using Bragg reflection of x rays, we can study colloidal crystals through Bragg scattering of visible light from the regular arrangement of charged microspheres. Because the light is traveling through a liquid when it experiences the path differences that lead to constructive interference, it is the wavelength in the liquid that determines the angles at which Bragg reflections are seen. In one experiment, laser light with a wavelength in vacuum of 650 nm is passed through a sample of charged polystyrene…arrow_forwardA colloid consists of particles of one type of substance dispersed in another substance. Suspensions of electrically charged microspheres (microscopic spheres, such as polystyrene) in a liquid such as water can form a colloidal crystal when the microspheres arrange themselves in a regular repeating pattern under the influence of the electrostatic force. Colloidal crystals can selectively manipulate different wavelengths of visible light. Just as we can study crystalline solids by using Bragg reflection of x rays, we can study colloidal crystals through Bragg scattering of visible light from the regular arrangement of charged microspheres. Because the light is traveling through a liquid when it experiences the path differences that lead to constructive interference, it is the wavelength in the liquid that determines the angles at which Bragg reflections are seen. In one experiment, laser light with a wavelength in vacuum of 650 nm is passed through a sample of charged polystyrene…arrow_forward
- A colloid consists of particles of one type of substance dispersed in another substance. Suspensions of electrically charged microspheres (microscopic spheres, such as polystyrene) in a liquid such as water can form a colloidal crystal when the microspheres arrange themselves in a regular repeating pattern under the influence of the electrostatic force. Colloidal crystals can selectively manipulate different wavelengths of visible light. Just as we can study crystalline solids by using Bragg reflection of x rays, we can study colloidal crystals through Bragg scattering of visible light from the regular arrangement of charged microspheres. Because the light is traveling through a liquid when it experiences the path differences that lead to constructive interference, it is the wavelength in the liquid that determines the angles at which Bragg reflections are seen. In one experiment, laser light with a wavelength in vacuum of 650 nm is passed through a sample of charged polystyrene…arrow_forwardA colloid consists of particles of one type of substance dispersed in another substance. Suspensions of electrically charged microspheres (microscopic spheres, such as polystyrene) in a liquid such as water can form a colloidal crystal when the microspheres arrange themselves in a regular repeating pattern under the influence of the electrostatic force. Colloidal crystals can selectively manipulate different wavelengths of visible light. Just as we can study crystalline solids by using Bragg reflection of x rays, we can study colloidal crystals through Bragg scattering of visible light from the regular arrangement of charged microspheres. Because the light is traveling through a liquid when it experiences the path differences that lead to constructive interference, it is the wavelength in the liquid that determines the angles at which Bragg reflections are seen. In one experiment, laser light with a wavelength in vacuum of 650 nm is passed through a sample of charged polystyrene…arrow_forwardLight of wavelength, 1 = 0.6 µm in air is incident on a thin sheet of transparent mylar (ɛ, = 6). (a) What is the wavelength of the light in mylar? (b) What thickness (1) gives minimum reflection? (c) If the mylar thickness is instead such that BI = T/2, what is the reflection coefficient, I ? Answers: (a) 2 = _ m %3| (b) l = _m %3D (c) T =, -arrow_forward
- A laser beam at a wavelength of 1.11 μm is coupled into an optic fiber, resulting in 138.2 mW of light inside the fiber initially. The fiber is 4.75 km long and has an absorption coefficienct of 1.562 dB/km. What light power, in mW, is at the end of the fiber?arrow_forwardTo reduce the loss of light when reflected from the glass surface, the latter is covered with a thin layer of a substance, the refractive index of which is n '= sqrt (n), where n is the refractive index of the glass. At what minimum thickness d (min) of this layer will the reflectivity of glass in the normal direction be minimal for light with a wavelength λ?arrow_forwardAt a wavelength 692 nm, the ordinary and extra-ordinary refractive indices in a uniaxial crystal are 1.558 and 1.611, respectively. If we make a thin disk of the material, with the optical axis parallel to the plane of the disk, what thickness of disk (in microns) would make a true zero-order quarter-wave plate?arrow_forward
- 10 mW of light is incident on a piece of GaAs which is 0.2mm thick. The incident light is a mixture of 5mW at λ1=1.553μm and 5mW at λ2=0.828μm. A total of 7mW mixed light exits out of the GaAs. Assume no reflections at the air/GaAs interface and any light generated by recombination won’t exit the GaAs. What are the absorption coefficients, α, for two different wavelengths?arrow_forwardA light-emitting diode made of a semiconductor material with a refractive index of 3.77 that emits light and bounces back at the interface between the semiconductor and the air. The angle at which the emitted light will be refracted is: (zero 0 45 degrees 0 30 degrees 0 90 degrees 0 above 0 the Not fromarrow_forward8.2-3 Parameters of a Dielectric Waveguide. Light of free-space wavelength A, = 0.87 um is guided by a thin planar film of widthd=2 um and refractive index n1 = 1.6 surrounded by a medium of refractive index n2 = 1.4. (a) Determine the critical angle 0, and its complement e, the numerical aperture NA, and the maximum acceptance angle for light originating in air (n = 1). (b) Determine the number of TE modes. (c) Determine the bounce angle 0 and the group velocity v of the m = 0 TE mode. Effect of Cladding, Repeat Prob. 8.2-3 if the thin film is suspended in air (no = 1), Compare 8.2-4arrow_forward
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