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A plane electromagnetic wave travelling in vacuum is incident normally on a non-magnetic, non-absorbing medium of refractive index n. The incident (Ei), reflected (Er) and transmitted (Et) electric fields are given as
Ei = E exp[i(kz - ωt)], Er = E0r exp[i(krz - ωt)], Et = E0t exp[i(ktz - ωt)]
If E = 2 V/m and n = 1.5, then the application of?
Ei = E exp[i(kz - ωt)], Er = E0r exp[i(krz - ωt)], Et = E0t exp[i(ktz - ωt)]
If E = 2 V/m and n = 1.5, then the application of?
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A plane electromagnetic wave travelling in vacuum is incident normally...
Understanding Plane Electromagnetic Wave Interaction
When a plane electromagnetic wave travels from vacuum into a non-magnetic, non-absorbing medium, several phenomena occur, including reflection and transmission. The wave equations for incident (Ei), reflected (Er), and transmitted (Et) electric fields highlight this interaction.
Key Wave Equations
- **Incident Wave (Ei)**:
\( E_i = E \exp[i(kz - \omega t)] \)
- **Reflected Wave (Er)**:
\( E_r = E_0^r \exp[i(-kz - \omega t)] \)
- **Transmitted Wave (Et)**:
\( E_t = E_0^t \exp[i(k_t z - \omega t)] \)
Here, \( E \) represents the amplitude of the incident wave, while \( E_0^r \) and \( E_0^t \) denote the amplitudes of the reflected and transmitted waves, respectively.
Refractive Index and Wave Parameters
Given that \( n = 1.5 \):
- The speed of light in the medium is \( v = \frac{c}{n} \), where \( c \) is the speed of light in vacuum. Thus, \( v = \frac{c}{1.5} \).
- The wave number in the medium is \( k_t = \frac{2\pi f}{v} = \frac{2\pi f n}{c} \).
Reflection and Transmission Coefficients
The reflection (\( R \)) and transmission (\( T \)) coefficients can be calculated as follows:
- **Reflection Coefficient (R)**:
\( R = \left| \frac{E_0^r}{E} \right|^2 = \left| \frac{n - 1}{n + 1} \right|^2 \)
- **Transmission Coefficient (T)**:
\( T = \left| \frac{E_0^t}{E} \right|^2 = \left| \frac{2}{n + 1} \right|^2 \)
For \( n = 1.5 \):
- \( R = \left| \frac{1.5 - 1}{1.5 + 1} \right|^2 = \left| \frac{0.5}{2.5} \right|^2 = \frac{1}{25} \)
- \( T = \left| \frac{2}{2.5} \right|^2 = \frac{4}{6.25} = \frac{16}{25} \)
This analysis emphasizes the behavior of electromagnetic waves at the interface of different media, encapsulating key concepts in optics.
When a plane electromagnetic wave travels from vacuum into a non-magnetic, non-absorbing medium, several phenomena occur, including reflection and transmission. The wave equations for incident (Ei), reflected (Er), and transmitted (Et) electric fields highlight this interaction.
Key Wave Equations
- **Incident Wave (Ei)**:
\( E_i = E \exp[i(kz - \omega t)] \)
- **Reflected Wave (Er)**:
\( E_r = E_0^r \exp[i(-kz - \omega t)] \)
- **Transmitted Wave (Et)**:
\( E_t = E_0^t \exp[i(k_t z - \omega t)] \)
Here, \( E \) represents the amplitude of the incident wave, while \( E_0^r \) and \( E_0^t \) denote the amplitudes of the reflected and transmitted waves, respectively.
Refractive Index and Wave Parameters
Given that \( n = 1.5 \):
- The speed of light in the medium is \( v = \frac{c}{n} \), where \( c \) is the speed of light in vacuum. Thus, \( v = \frac{c}{1.5} \).
- The wave number in the medium is \( k_t = \frac{2\pi f}{v} = \frac{2\pi f n}{c} \).
Reflection and Transmission Coefficients
The reflection (\( R \)) and transmission (\( T \)) coefficients can be calculated as follows:
- **Reflection Coefficient (R)**:
\( R = \left| \frac{E_0^r}{E} \right|^2 = \left| \frac{n - 1}{n + 1} \right|^2 \)
- **Transmission Coefficient (T)**:
\( T = \left| \frac{E_0^t}{E} \right|^2 = \left| \frac{2}{n + 1} \right|^2 \)
For \( n = 1.5 \):
- \( R = \left| \frac{1.5 - 1}{1.5 + 1} \right|^2 = \left| \frac{0.5}{2.5} \right|^2 = \frac{1}{25} \)
- \( T = \left| \frac{2}{2.5} \right|^2 = \frac{4}{6.25} = \frac{16}{25} \)
This analysis emphasizes the behavior of electromagnetic waves at the interface of different media, encapsulating key concepts in optics.
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A plane electromagnetic wave travelling in vacuum is incident normally on a non-magnetic, non-absorbing medium of refractive index n. The incident (Ei), reflected (Er) and transmitted (Et) electric fields are given asEi = E exp[i(kz - ωt)], Er = E0r exp[i(krz - ωt)], Et = E0t exp[i(ktz - ωt)]If E = 2 V/m and n = 1.5, then the application of?
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