Transmission coefficient and the reflection coefficient

In summary, the conversation discusses the calculation of the transmission and reflection coefficients for a particle approaching a sudden change in potential. The transmission coefficient is found to be dependent on the ratio of the particle's wavelength, rather than the wavelength itself. A graph is shown to illustrate this relationship, with a turning point at a=1, corresponding to 100% transmission. However, for a potential approaching infinity, the graph shows 0% transmission, which may suggest that a macroscopic object would also experience reflection. The validity of this interpretation is questioned, and it is suggested that the solution should be reworked to verify the results.
  • #1
jby
I tried to work out the transmission coefficient and
the reflection coefficient for a case similar to the
one referred by this website:
http://www.chembio.uoguelph.ca/educmat/chm386/rudiment/models/barrier/barsola.htm [Broken]

but instead this time, I reverse the situation and
now, that particle I is heading from the right, ie
from a higher potential and a possibility that it will
be transmitted to the left, ie to a lower potential,
still with the same E > V.

I've drawn a diagram of the situation which I am
considering in my question using my own notations.
(As this is a bmp file, it may take some time to
load.)

http://www.geocities.com/ace_on_mark9909/reflection.htm


My confusion is regarding to the reflection and its
coefficient, which I've worked in steps here:

I state here the situation I am referring to: Supposing
the particle initially is at the potential V = 0,
heading to the left. At x = 0, there is the sudden
change in the potential to V = -V'.

Using p as the wave number, ie (2pi/lambda) for the
particle when at V = 0, and q as wave number for
particle at V = -V', I obtained the transmission
coefficient, T as 4pq/(p+q)^2.

By the condition of the potential 0 > -V', thus, p <
q, ie the wavelength at V = 0 > wavelength at V = -V'.


Let, q = ap, ie a = ratio of final wavenumber to
initial wave number: q/p. Since, q > p => a > 1.

We simplify the transmission coefficient to from
T = 4pq/(p+q)^2
to
T = 4a/(1+a)^2 ... (1)

From equation 1, it states that T is only dependent on
the ratio of the two wave number and hence dependent
only on the ratio of both wavelengths, and not on any
of the wavelength alone

=> the coefficient T does not discriminate on the size
on any of the wavelength alone but the ratio of the
magnitude of its wavelengths.

=> T does not distinguish between a particle or a
macroscopic object, eg, a ball.

From T = 4a/(1+a)^2, I've drawn a graph of it for a in
the range 0 <= a <= +infinity. I've uploaded to this
website:

http://www.geocities.com/ace_on_mark9909/transmission.htm


From the graph, it looks like there is a turning point
at a = 1, corresponding to T = 1, and slowly goes to
zero, as a -> infinity

By a -> infinity, we can say that the potential height
-V' approaches -infinity.

But, if the potential at x = 0, changes so sharply as
in approaching infinity, the graph shows T = 0, then,
it means that if I were to replace a particle with a
ball/human and is to approach this potential it is
almost likely to be reflected back...

Is there anything wrong with my maths? If not, how do
you interpret this result?
 
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  • #2
This thread got no love in the Homework forum, so I'm kicking it here to Physics.
 
  • #3
The energy of a macroscopic object is going to be so great that the potential isn't going to matter and your going to get complete transmission.

JMD

You should rework the solution, beacuse I doubt you get any reflection, but I haven't worked this out for a few years and can't remember right of the top of my head.
 
Last edited:

1. What is the difference between the transmission coefficient and the reflection coefficient?

The transmission coefficient is a measure of the amount of energy that passes through a boundary between two mediums, while the reflection coefficient is a measure of the amount of energy that is reflected back from the boundary. In other words, the transmission coefficient represents the fraction of energy that is transmitted through the boundary, while the reflection coefficient represents the fraction of energy that is reflected.

2. How are the transmission coefficient and reflection coefficient related?

The transmission and reflection coefficients are related by the law of conservation of energy. This means that the sum of the transmission and reflection coefficients is always equal to one. Therefore, if one coefficient increases, the other must decrease.

3. What factors affect the transmission and reflection coefficients?

The transmission and reflection coefficients are affected by the properties of the two mediums that the boundary separates, such as their refractive indices and the angle of incidence. The type of wave, whether it is electromagnetic or mechanical, also plays a role in determining these coefficients.

4. How are the transmission and reflection coefficients calculated?

The transmission and reflection coefficients can be calculated using the Fresnel Equations, which take into account the properties of the two mediums and the angle of incidence. These equations are different for electromagnetic and mechanical waves.

5. What is the practical application of the transmission and reflection coefficients?

The transmission and reflection coefficients are important in understanding and predicting the behavior of waves at boundaries between different mediums. This knowledge is essential in fields such as optics, acoustics, and electronics, and is used in the design of various devices such as lenses, mirrors, and filters.

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