@rude man Please study my solution in detail, and I think you will see where the OP misses what is basically a ## -2ka ## term that needs to be included in the OP's solution. ## \\ ## Editing: I specialized in Optics (Diffraction and Interference theory, etc.) and Spectroscopy as a graduate student in college, so that it would be somewhat embarrassing if I didn't have it correct. :)rude man said:
IMO, the author of the book probably has limited expertise in Optics and Interference and Diffraction theory. It isn't real surprising that he might have an incorrect answer for such a problem. Unless a physics person actually specializes in this kind of thing, it would be quite easy for them to get an incorrect result for the solution. If they thought the problem was identical to a water wave bouncing off a wall, then ## E_{reflected}(a,t)=E_{incident}(a,t) ##. In addition, it would be easy for someone who doesn't specialize in this type of thing to miss the ## -2 k a ## phase term that results when the barrier is not at ## z=0 ##. I give them credit for what I think was an honest mistake or two in their solution. ## \\ ## As for the minus sign out in front, there are two ways to explain it: There is an electromagnetic boundary condition that ## E_{air \, total}(a,t)=E_{incident}(a,t)+E_{reflected}(a,t)=E_{transmitted}(a,t) =0 ##, so that ## E_{reflected}(a,t)=-E_{incident}(a,t) ##. For an alternate derivation, the Fresnel reflection coefficient ## \rho=(n1-n2)/(n1+n2) ##. For a metal, ## n2 ## has a very large complex term to it,(and ## n1=1 ##) , so that ## \rho=-1 ## (or very nearly so), where ## \rho=\frac{E_{reflected}(a,t)}{E_{incident}(a,t)} ##.Jahnavi said:
You have not included phase shift pi in your calculationJahnavi said:
Minus is here for change in direction of electric field after reflectionCharles Link said:
The direction of the wave is determined by the relative sign between the ## kz ## term and the ## \omega t ## term. If they are different, the wave travels in the positive z direction (to the right), e.g. (## \cos(kz-\omega t) ##). If they are the same, the wave travels to the left (e.g. ## \cos( kz+\omega t) ##).Delta² said:
Delta² said:
Agreed! I missed the part about reflection at z=a .Charles Link said:
Posts 6 and 11 are the best explanation I can offer for what I think is definitely an incorrect answer that the author provides. :)Jahnavi said:Change of phase is not an issue in this problem
There is definitely a change of phase of π since the reflection is from an optically inactive surface . I am assuming this to be optically denser medium . Right @Charles Link .
And since the wave is traveling in opposite direction , (kz-wt) changes to (kz+wt) . Taking both of these in consideration , I am getting an extra minus sign which answer doesn't have .
The minus sign will essentially change the phase of the reflected wave by ## \pi ## (## =180^o ##), because ## -\cos(kz+\omega t)=\cos(kz+\omega t + \pi) ## . (Use ## \cos(\theta+\phi)=\cos(\theta) \cos(\phi)-\sin(\theta) \sin(\phi) ## identity to show this). The minus sign is correct, if the reflective material is assumed to be of a higher index ## n ##.Jahnavi said:
.It is apparent that the author of the book is not an expert on this topic. It's always very helpful when the book teaches it correctly=this kind of inaccuracies can have a lot of students spinning their wheels unnecessarily. At least the Physics Forums is available that can most often supply the correct result when such a thing is encountered. :)Jahnavi said:Ok.
I am attaching the solution given in the book . In case you feel there is a printing error in the options then you will be in for a surprise
Please see if you can understand it .
The confusing part is changing of i to -i in the reflected wave .
Same thing i have mentioned in post 8 and 10.direction of electric and magnetic field will also reverse.Jahnavi said:Ok.
I am attaching the solution given in the book . In case you feel there is a printing error in the options then you will be in for a surprise
Please see if you can understand it .
The confusing part is changing of i to -i in the reflected wave .
The reflected wave has a - sign because when you ADD Ei and Er the - sign is needed. Superposition is addition so to get cancellation at z=a you need the - sign, otherwise you'd get double instead of zero at z=a.Jahnavi said:
rude man said:
You have to consider at the instant of reflection.it will cancel outJahnavi said:
Abhishek kumar said:
You are only considering position not time.when incident wave traveled a unit reflected wave just startedJahnavi said:
Abhishek kumar said:
Yes, the incident wave and reflected wave add up to zero at the interface at any instant. t is the same in both waves.Jahnavi said:
Read standing wave form by super position of reflected and incident waveJahnavi said:
Jahnavi said:
That's what i want to sayDelta² said:
Abhishek kumar said:
Abhishek kumar said:
You have taken same distance traveled by both the wave at any instant of time is it possible?that's why i said you r considering only same position.For same time position will be differentJahnavi said:This is not what you said in post 27
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.
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.
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.
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.
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.
