the author 
"Frustrated Total Internal Reflection"
Nick Armstrong, Head of Physics, The Edinburgh Academy
Abstract: Quantum Mechanics is appearing with increasing regularity in modern post 16 Physics syllabuses.
Teaching abstract concepts is made much easier if there are appropriate physical models to refer to or practical activities to help a student’s understanding.
This article highlights a practical approach to illustrate one of quantum mechanics most surprising results, namely "Tunnelling".
Frustrated Total Internal Reflection
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Total Internal Reflection is a phenomenon which is familiar to many students studying a course of Physics pre 16 (as detailed in U.K. syllabuses from AQA [1] and OCR [2]). A typical experimental scenario is illustrated in Fig 1. Light (i.e. the visible part of the electromagnetic spectrum) is used in the demonstration but any wave form could in theory be used. |
No light is detected beyond the glass at the position X indicated by the block arrow (and no more is said to most students!). However, a solution to Maxwell’s wave equation does exist at this point. The solution indicates that the Electric field of the E-M wave will decay exponentially at this point rather than oscillate in a sinusoidal fashion as it does inside the glass (see Bleaney and Bleaney [3]). If the electric field is finite then it must have some meaning but possibly a rather abstract one. "The conventional unit for electric field strength is the square root of a joule per cubic metre" (Dyson [4]) i.e. it is the square of this quantity (electric field) which is measurable (in the same way that it is the square of the solution to Schrodinger’s equation which has some physical meaning). It can be shown that the size of the electric field at X in Fig 1, has diminished to almost zero at about one wavelength from the glass. Measurement of this field (or even the square of the field) would be difficult because of the small distances involved. However, if microwaves are used instead of light, the distances now make measurements possible. Many school Physics departments will have or have access to "3 cm" microwave apparatus. Wax prisms and lenses are available with the wax having a refractive index of about 1.5 at the microwave frequencies. The procedure for demonstrating frustrated total internal reflection is as follows: |
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Fig 2 Normal Total Internal Reflection (The wax lens helps to produce a collimated beam of microwaves but is not essential.) |
Repeating the experimentThe experiment is then repeated using two prisms as shown in figure 3. |
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Fig 3 Frustrated Total Internal Reflection |
Microwaves cannot be detected in the gap between the prisms (because the electric field is not oscillating) but they can be detected by the receiver to the right of the prisms (solving Maxwell’s equation inside the second prism and beyond produces an oscillating electric field). If the microwave beam is considered to be a beam of "photons" then some of the photons must have "tunnelled" through the gap between the two prisms (a forbidden region) and appear passing through the second prism.
The intensity of the microwaves detected to the right of the prisms decreases rapidly with increasing separation of the prisms in accordance with the idea that the electric field decays exponentially between the prisms. Testing the exponential decay is not straight forward, however, because most microwave detectors have a non-linear response ie the output is not directly proportional to the intensity of the received microwaves.
Prior calibration of the equipment followed by an experiment could form the basis of an extended study for a suitable post 16 student.
This page is: Edinburgh Academy / curriculum /physics/staffwork.htm
