Can the transmission coefficient tau can ever be negative? Justify your answer.
ID: 3162810 • Letter: C
Question
Can the transmission coefficient tau can ever be negative? Justify your answer. Can the height of a transmitted pulse ever be larger than the height of an incident pulse? Justify your answer. What will be the reflection coefficient rho in the limit that Z_2/Z_1 rightarrow 0? What will be the reflection coefficient rho in the limit that Z_1/Z_2 rightarrow 0? What will be the reflectance R in the limit that Z_2/Z_1 rightarrow 0? What will be the reflectance R in the limit that Z_1/Z_2 rightarrow 0?Explanation / Answer
A) Considering discontinuity the transmission coeffcient describes the amount of EM wave pass through an suitable media. Now for EM wave if we use boundary condition then first of all we notice that transmission wave is the sum of reflected and incident waves.
Et=Ei+Er
Taking phase velocity as the function of wave vector and frequency we can write
Er=(n1-n2/n1+n2)*Ei
Et= 2n1/(n1+n2)*Ei
where n1 and n2 are the R.I of incident and reflected plane.
Now we consider different situations like n1=n2 that means Er=0 but Et=Ei
which shows two planes of same R.I so no reflection in the boundary. Again if n2>n1 we get 180degree shift of reflected wave annd no shift for n1>n2.
In case of perfectly reflecting interface we can get reflecting coefficient both positive and negative making transmission coefficient 0 or more than 1 but negative transmission coefficient means the passing direction is opposite therefore it is not possible.
b)From the boundary behaviour the incident light is divided into reflected and transmitted part and that means if the light is moving from less dense to high dense plane the speed and wavelength will be small. so transmitted wavelength is smaller than incident wavelength. Now from high dense to less dense medium the light speed is higher so the wavelength can bee greater than incident wave.
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