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# 物理代写|光学代考Optics代写|CSCI031 Equations and parameters of electromagnetic waves

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## 物理代写|光学代考Optics代写|Equations and parameters of electromagnetic waves

Estimate the phase velocity $v$ of light propagation in a medium with refractive index $n=1.5$. Determine the wavelength $\lambda$ of the light in this medium if the frequency of the light oscillations is $v=5 \cdot 10^{14} \mathrm{~Hz}$.
Determine the change $\Delta v$ of the phase velocity of light propagation due to refraction at the interface between glass $\left(n_1=1.5\right)$ and water $\left(n_2=1.33\right)$, and the ratio of wavelengths $\lambda_1 / \lambda_2$.
Determine the phase velocity $v$ of light propagation in a medium with relative permittivity $\varepsilon=2.5$ and permeability $\mu=1$.
Show that the plane-wave expression $E(z, t)=E_0 \cos (\omega t-k z)$ is a solution of the wave equation and express the phase velocity of the wave $v$ in terms of the wave parameters, namely, circular frequency $\omega$ and spatial circular frequency (wave number) $k$.
Using the complex form of the expression for a plane harmonic wave propagating along the $z$ axis, show that this expression satisfies the wave equation.
Using the complex expression for the plane harmonic electromagnetic wave and Maxwell’s equations in the differential form, show that the vectors $\vec{E}, \vec{H}$ and $\vec{k}$ of the wave form the right-hand trio of mutually perpendicular vectors in isotropic dielectric media.
The plane-harmonic wave in a certain medium is described by the expression $E(z, t)=5 \cos \left(2 \pi \cdot 5 \cdot 10^{14} \cdot t-\frac{2 \pi}{0.4 \cdot 10^{-6}} \cdot z\right)$. Determine the circular frequency $\omega$, the wavelength $\lambda$, the phase velocity of the wave $v$, and the refractive index of the medium $n$.
Determine the phase difference $\Delta \phi_{12}$ between the oscillations excited by the plane wave with wavelength $\lambda$, propagating along the $z$ axis, at points $\mathrm{P}_1$ and $\mathrm{P}_2$ with coordinates $z_1$ and $z_2$.

## 物理代写|光学代考Optics代写|Spectral properties of electromagnetic waves

The spectral contour of quasi-monochromatic light has a half-width $\Delta \lambda \approx 0.01 \mu \mathrm{m}$ at the central wavelength $\lambda_0 \approx$ $600 \mathrm{~nm}$. Determine the temporal coherence length $l_c$ and the coherence time $\tau_c$ of such light.
Determine the coherence time $\tau_c$ and the length of the wave train $l_c$ of the electromagnetic wave in a medium with refractive index $n=1.5$ if the half-width of the frequency contour of this wave is $\Delta v \approx 10^{13} \mathrm{~Hz}$.
Determine the mean number of oscillations $m$ in a singlewave train of the radiation of a red light-emitting diode with mean wavelength $\lambda_0 \approx 0.65 \mu \mathrm{m}$ and spectral contour width $\Delta \lambda \approx 20 \mathrm{~nm}$, and the radiation of a helium-neon gas laser with $\lambda_0 \approx 0.63 \mu \mathrm{m}$ and $\Delta \lambda \approx 0.04 \mathrm{~nm}$.
White light is passed through an optical filter F. The spectralcontour width of the white light is $\Delta \lambda \approx 150 \mathrm{~nm}$ and the central wavelength is $\lambda_0 \approx 0.55 \mu \mathrm{m}$. The central wavelength of the filter transmission band is $\lambda_f \approx 0.65 \mu \mathrm{m}$ and transmission bandwidth is $\Delta \lambda_f \approx 15 \mathrm{~nm}$. Determine the ratio of coherence lengths (lengths of wave train) after and before the filter.

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## 物理代写|光学代考Optics代写|Spectral properties of electromagnetic waves

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