## A table top experiment with polaroids

We have discussed the polarisation of light in Section 8.12 from the wave theory point of view, representing the polaroids material schematically as a 'slit' which allows only the component of vibrations parallel to it to get through. The emerging light is then represented as consisting of electric field oscillations only in the direction of the slit. If the light then comes to a second polaroid with its axis inclined at an angle 0 to the first, the intensity of the light emerging is reduced by a factor cos20. In the case when the axes are perpendicular ('crossed polaroids'), no light gets through.

We will now consider the phenomenon in terms of the particle model. Each polaroid is represented as a mechanism for measuring a certain property of a photon called 'polarisation'. Any photon which is transmitted through a '0 polaroid' has the property that it will pass through any other '0 polaroid', but has only a limited probability of transmission through a polaroid oriented at any other angle. This probability is equal to cos2A0, where A0 is the difference between the inclination of the two slits. (Malus's law)

Let us start with just two polaroids, with axes of polarisation at 90° to one another, which we will call the 'X polaroid' and the 'Y polaroid'. A photon which has 'passed the test' of the X polaroid, and then comes to the Y polaroid, will certainly 'fail' this second test, and be absorbed. This is the standard 'crossed polaroid' effect.

Let us next introduce the third, randomly oriented polaroid — the 'R polaroid' — between the other two, and let us call its angle of orientation 0. By inserting the random polaroid we are making a new measurement which is a test to see if the 'X photon' passes through the R polaroid. If it passes this test it becomes a photon with angle of polarisation 0 relative to the X direction. It 'forgets' that it had ever been a X photon and becomes a '0 photon'.

What happens when a '0 photon' meets the Y polaroid, i.e. the second of the two original crossed polaroids. This was the test we knew was going to fail in the original system. Now we are not sure! It may or may not pass this next test. The probability depends on the angle 0 and, according to Malus's law, is proportional to cos2 (90° - 0).

By inserting another obstacle into the path of the photon, we give it a chance to pass through the system. Paradoxically the extra fence has made the passage easier and not harder (Figure 12.1).

Y-polaroid

X-polaroid

Y-polaroid

X-polaroid

R polaroid

R polaroid

X-photon cannot get through the Y-polaroid unless we give it a random polarisation test!

X-photon cannot get through the Y-polaroid unless we give it a random polarisation test!

Figure 12.1 An experiment with polaroids.

What we have learned from the experiment:

1. The order in which we make observations matters. The result is quite different if we place the random polaroid in front of or behind the other two.

2. The photon behaves as a typical 'quantum particle'. An observed photon is not the same as it was before it was observed. This is something we shall discuss later.

This experiment can be performed using the simplest of equipment, and a normal light source, such as sheets of polaroid placed on an overhead projector.

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