Answer:
Wavelength of the incident wave in air = 1 m
Wavelength of the incident wave in medium 2 = 0.33 m
Intrinsic impedance of media 1 = 377 ohms
Intrinsic impedance of media 2 = 125.68 ohms
Check the explanation section for a better understanding
Explanation:
a) Wavelength of the incident wave in air
The frequency of the electromagnetic wave in air, f = 300 MHz = 3 * 10⁸ Hz
Speed of light in air, c = 3 * 10⁸ Hz
Wavelength of the incident wave in air:
![\lambda_{air} = \frac{c}{f} \\\lambda_{air} = \frac{3 * 10^{8} }{3 * 10^{8}} \\\lambda_{air} = 1 m](https://tex.z-dn.net/?f=%5Clambda_%7Bair%7D%20%3D%20%5Cfrac%7Bc%7D%7Bf%7D%20%5C%5C%5Clambda_%7Bair%7D%20%3D%20%5Cfrac%7B3%20%2A%2010%5E%7B8%7D%20%7D%7B3%20%2A%2010%5E%7B8%7D%7D%20%5C%5C%5Clambda_%7Bair%7D%20%3D%201%20m)
Wavelength of the incident wave in medium 2
The refractive index of air in the lossless dielectric medium:
![n = \sqrt{\epsilon_{r} } \\n = \sqrt{9 }\\n =3](https://tex.z-dn.net/?f=n%20%3D%20%5Csqrt%7B%5Cepsilon_%7Br%7D%20%7D%20%5C%5Cn%20%3D%20%5Csqrt%7B9%20%7D%5C%5Cn%20%3D3)
![\lambda_{2} = \frac{c}{nf}\\\lambda_{2} = \frac{3 * 10^{6} }{3 * 3 * 10^{6}}\\\lambda_{2} = 1/3\\\lambda_{2} = 0.33 m](https://tex.z-dn.net/?f=%5Clambda_%7B2%7D%20%3D%20%5Cfrac%7Bc%7D%7Bnf%7D%5C%5C%5Clambda_%7B2%7D%20%3D%20%5Cfrac%7B3%20%2A%2010%5E%7B6%7D%20%7D%7B3%20%2A%203%20%2A%2010%5E%7B6%7D%7D%5C%5C%5Clambda_%7B2%7D%20%3D%201%2F3%5C%5C%5Clambda_%7B2%7D%20%3D%200.33%20m)
b) Intrinsic impedances of media 1 and media 2
The intrinsic impedance of media 1 is given as:
![n_1 = \sqrt{\frac{\mu_0}{\epsilon_{0} } }](https://tex.z-dn.net/?f=n_1%20%3D%20%5Csqrt%7B%5Cfrac%7B%5Cmu_0%7D%7B%5Cepsilon_%7B0%7D%20%7D%20%7D)
Permeability of free space, ![\mu_{0} = 4 \pi * 10^{-7} H/m](https://tex.z-dn.net/?f=%5Cmu_%7B0%7D%20%3D%204%20%5Cpi%20%2A%2010%5E%7B-7%7D%20H%2Fm)
Permittivity for air, ![\epsilon_{0} = 8.84 * 10^{-12} F/m](https://tex.z-dn.net/?f=%5Cepsilon_%7B0%7D%20%3D%208.84%20%2A%2010%5E%7B-12%7D%20F%2Fm)
![n_1 = \sqrt{\frac{4\pi * 10^{-7} }{8.84 * 10^{-12} } }](https://tex.z-dn.net/?f=n_1%20%3D%20%5Csqrt%7B%5Cfrac%7B4%5Cpi%20%2A%2010%5E%7B-7%7D%20%20%7D%7B8.84%20%2A%2010%5E%7B-12%7D%20%20%7D%20%7D)
![n_1 = 377 \Omega](https://tex.z-dn.net/?f=n_1%20%3D%20377%20%5COmega)
The intrinsic impedance of media 2 is given as:
![n_2 = \sqrt{\frac{\mu_r \mu_0}{\epsilon_r \epsilon_{0} } }](https://tex.z-dn.net/?f=n_2%20%3D%20%5Csqrt%7B%5Cfrac%7B%5Cmu_r%20%5Cmu_0%7D%7B%5Cepsilon_r%20%5Cepsilon_%7B0%7D%20%7D%20%7D)
Permeability of free space, ![\mu_{0} = 4 \pi * 10^{-7} H/m](https://tex.z-dn.net/?f=%5Cmu_%7B0%7D%20%3D%204%20%5Cpi%20%2A%2010%5E%7B-7%7D%20H%2Fm)
Permittivity for air, ![\epsilon_{0} = 8.84 * 10^{-12} F/m](https://tex.z-dn.net/?f=%5Cepsilon_%7B0%7D%20%3D%208.84%20%2A%2010%5E%7B-12%7D%20F%2Fm)
ϵr = 9
![n_2 = \sqrt{\frac{4\pi * 10^{-7} *1 }{8.84 * 10^{-12} *9 } }](https://tex.z-dn.net/?f=n_2%20%3D%20%5Csqrt%7B%5Cfrac%7B4%5Cpi%20%2A%2010%5E%7B-7%7D%20%2A1%20%7D%7B8.84%20%2A%2010%5E%7B-12%7D%20%2A9%20%7D%20%7D)
![n_2 = 125.68 \Omega](https://tex.z-dn.net/?f=n_2%20%3D%20125.68%20%5COmega)
c) The reflection coefficient,r and the transmission coefficient,t at the boundary.
Reflection coefficient, ![r = \frac{n - n_{0} }{n + n_{0} }](https://tex.z-dn.net/?f=r%20%3D%20%5Cfrac%7Bn%20-%20n_%7B0%7D%20%7D%7Bn%20%2B%20n_%7B0%7D%20%7D)
You didn't put the refractive index at the boundary in the question, you can substitute it into the formula above to find it.
![r = \frac{3 - n_{0} }{3 + n_{0} }](https://tex.z-dn.net/?f=r%20%3D%20%5Cfrac%7B3%20-%20n_%7B0%7D%20%7D%7B3%20%2B%20n_%7B0%7D%20%7D)
Transmission coefficient at the boundary, t = r -1
d) The amplitude of the incident electric field is ![E_{0} = 10 V/m](https://tex.z-dn.net/?f=E_%7B0%7D%20%3D%2010%20V%2Fm)
Maximum amplitudes in the total field is given by:
and ![E = r E_{0}](https://tex.z-dn.net/?f=E%20%3D%20r%20E_%7B0%7D)
E = 10r, E = 10t