## Feynmans strange theory of the photon 1421 Partial reflection

We saw in Chapter 3 that Isaac Newton was deeply puzzled by the fact that when light strikes a boundary between two media, part of it is reflected and part of it enters the second medium. Looking at this from the point of view of a photon, its fate is not pre-determined. It has a certain probability of 'bouncing back',

/ photo multiplier

Figure 14.7 Partial reflection of single photons.

and a certain probability of penetrating into the second medium. This is a typical quantum-mechanical situation.

Let us follow Richard Feynman's account of his formulation of quantum electrodynamics by considering the partial reflection of single photons. Such photons, well separated in space, arrive at a boundary between air and glass, as illustrated in Figure 14.7.

Suppose we find that out of 100 photons which strike the glass surface, on the average, 96 are transmitted and 4 are reflected.

Let us consider in detail what seems to be happening. The photons arrive at the surface one by one. They are all identical. What causes a particular photon to be reflected and another to be transmitted? Perhaps there are some local imperfections in the glass surface, grains that reflect the photon and holes that let it through? Let us stick with that theory for the moment.

Let us now replace the block of glass by a thin sheet of glass. We find that when the photons come to the second surface, a similar thing happens. Some photons are transmitted and get back out into the air while others are reflected back into the

A possible theory: If a photon hits a grain of microscopic or atomic dimensions, it is reflected; otherwise it continues on into the glass.

photo multiplier

multiplier

Figure 14.8 What we expect is not what we get.

glass. The relative percentage reflected and transmitted is the same as at the first surface.

The photomultiplier counts photons reflected from both surfaces. This figure is similar to Figure 8.13 in Chapter 8, when we were dealing with the reflection of light waves from thin films. This time, however, we are dealing with individual photons; we hear a 'click' as each photon enters the photomultiplier.

If 4 photons out of 100 are reflected at the first surface, we might expect 8 photons or slightly less to reach the photomulti-plier after 2 reflections. (Slightly less because the original beam of 100 photons has decreased to 96 photons reaching the second surface, and then gets attenuated again when it meets the first surface again on the way back.)

The result of this experiment negates any simple theory of grains or imperfections at each surface; it is not at all what we expected. Sometimes the photomultiplier registers no clicks whatsoever, and sometimes there are as many as 16 photons! It all depends on the thickness of the glass.

What we expect is not what we get!

Warning: Another surface / distance t below

Warning: Another surface / distance t below

Figure 14.9 When a photon arrives at the glass surface, its decision on whether to reflect or continue is influenced by how far it is to the second surface.

Even individual photons behave as waves!

In Chapter 8 we were able to explain the phenomenon of reflection of light by thin films on the basis of interference between the two waves reflected at the first and the second surface. We now find the same result when we are dealing with individual photons! They register as clicks of the photomultiplier, i.e. behave as particles, yet at the same time they follow the rules of waves. The photon has two faces — we can see one or the other, depending on how we look at it!

Remember the analogy?

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