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Chapter 6: Q4CQ (page 223)

The equations for Rand T in the E>U0barrier essentially the same as light through a transparent film. It is possible to fabricate a thin film that reflects no light. Is it possible to fabricate one that transmits no light? Why? Why not?

Short Answer

Expert verified

The answer is no.

Step by step solution

01

Defining the condition

In the given condition, the transmission probability is zero for the numerator being zero. This is possible only if U0tends to ±∞.

T=4EU0EU0-1sin22mE-U0Lℏ+4EU0EU0-1∣

02

Explanation and conclusion

For a wave, it becomes difficult to reflect from a non-infinite potential without another wave being on the opposite side. Thus, in bouncing back and forth from barrier, some parts of wave are lost as transmitted energy at x=Lwall. And when boundary are applied, the solutions do not match forx<Landx>L.

So, it is not possible to fabricate a thin film which transmits no light.

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