Phase Change and Reflection of Electromagnetic Waves

Thread starter Jahnavi
Start date Dec 20, 2017
Tags

Em Em wave Reflection Wave

In summary: Therefore, the reflected wave is E = -E0icos (kz + ωt). However, this is incorrect. Upon working through the problem in its entirety, we get the solution E = E0icos (kz + ωt), which matches option B without the minus sign. It is possible that the question setter made some simplified assumptions that led to the incorrect solution, but the correct answer is E = E0icos (kz + ωt) without any minus sign. This may be due to a misunderstanding of electromagnetic boundary conditions or the Fresnel reflection coefficient. Overall, it is important to carefully consider all factors and assumptions when solving problems in order to arrive at the correct solution.

Dec 21, 2017

Charles Link

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Jahnavi said:

At z = a , E₀cos (ka- ωt) - E₀cos (ka + ωt) = 2E₀sin(ka)sin(ωt) ≠ 0

Can you show how they cancel ?

@Jahnavi I think you have this part figured out already, but to show it in detail: ## \\ ## ## E_{incident}(z,t)=E_o \hat{i} \cos(kz-\omega t) ##, and ## \\ ## ## E_{reflected}(z,t)=-E_o \hat{i} \cos(2ka-kz-\omega t) ##. ## \\ ## Evaluating at ## z=a ##: ## \\ ## ## E_{incident}(a,t)=E_o \hat{i} \cos(ka-\omega t) ##, and ## \\ ## ## E_{reflected}(a,t)=-E_o \hat{i} \cos(2ka-\omega t-ka)=-E_o \hat{i} \cos(ka-\omega t) ##. ## \\ ## Thereby, they cancel at ## z=a ##. ## \\ ## Also, in post 21, you asked about the vector ## \hat{i} ##. Yes, that means the electric field for this electromagnetic wave is transverse and points in the x-direction.

Last edited: Dec 21, 2017

<h2>1. What is a phase change in the context of electromagnetic waves?</h2><p>A phase change in electromagnetic waves refers to the change in the relative position of the crests and troughs of the wave. This can occur when the wave travels from one medium to another, such as from air to water, and experiences a change in its speed. Phase changes can also occur when the wave reflects off a surface.</p><h2>2. How does the phase change affect the behavior of electromagnetic waves?</h2><p>The phase change can affect the behavior of electromagnetic waves in several ways. For example, when a wave reflects off a surface, the phase change can cause interference patterns to form, resulting in constructive or destructive interference. In addition, phase changes can also affect the polarization of the wave, which is the direction in which the electric field oscillates.</p><h2>3. What is the relationship between phase change and frequency of electromagnetic waves?</h2><p>The relationship between phase change and frequency of electromagnetic waves is that they are inversely proportional. This means that as the frequency of a wave increases, the phase change decreases, and vice versa. This relationship is described by the equation λ = c/f, where λ is the wavelength, c is the speed of light, and f is the frequency.</p><h2>4. How does the angle of incidence affect the phase change of reflected electromagnetic waves?</h2><p>The angle of incidence, which is the angle at which a wave hits a surface, can affect the phase change of reflected electromagnetic waves. When the angle of incidence is equal to the angle of reflection, the phase change is zero and the wave is said to be in phase. However, when the angle of incidence is different from the angle of reflection, the phase change will occur and the wave will be out of phase.</p><h2>5. Can the phase change of electromagnetic waves be controlled?</h2><p>Yes, the phase change of electromagnetic waves can be controlled through various means. One way is by using materials with different refractive indices, which can cause a phase change when the wave travels through them. Another way is by using devices such as phase shifters, which can adjust the phase of a wave. This control over phase change is important in many applications, such as in telecommunications and imaging technologies.</p>

1. What is a phase change in the context of electromagnetic waves?

A phase change in electromagnetic waves refers to the change in the relative position of the crests and troughs of the wave. This can occur when the wave travels from one medium to another, such as from air to water, and experiences a change in its speed. Phase changes can also occur when the wave reflects off a surface.

2. How does the phase change affect the behavior of electromagnetic waves?

The phase change can affect the behavior of electromagnetic waves in several ways. For example, when a wave reflects off a surface, the phase change can cause interference patterns to form, resulting in constructive or destructive interference. In addition, phase changes can also affect the polarization of the wave, which is the direction in which the electric field oscillates.

3. What is the relationship between phase change and frequency of electromagnetic waves?

The relationship between phase change and frequency of electromagnetic waves is that they are inversely proportional. This means that as the frequency of a wave increases, the phase change decreases, and vice versa. This relationship is described by the equation λ = c/f, where λ is the wavelength, c is the speed of light, and f is the frequency.

4. How does the angle of incidence affect the phase change of reflected electromagnetic waves?

The angle of incidence, which is the angle at which a wave hits a surface, can affect the phase change of reflected electromagnetic waves. When the angle of incidence is equal to the angle of reflection, the phase change is zero and the wave is said to be in phase. However, when the angle of incidence is different from the angle of reflection, the phase change will occur and the wave will be out of phase.

5. Can the phase change of electromagnetic waves be controlled?

Yes, the phase change of electromagnetic waves can be controlled through various means. One way is by using materials with different refractive indices, which can cause a phase change when the wave travels through them. Another way is by using devices such as phase shifters, which can adjust the phase of a wave. This control over phase change is important in many applications, such as in telecommunications and imaging technologies.