# Polarisation PLUS

**This explanation is intended to serve as an addition to the main explanation.**

Additional points to include when demonstrating to taller than average children (use your own judgement as to how interested the students are, and which topics are appropriate to their subject area - sometimes it might be better to stick to the main explanation):

## Malus's Law

For students interested in maths and physics, you can derive Malus's Law for the intensity of light transmitted through a polarising filter - which is that the transmitted intensity is cos^2(θ) relative to the incident intensity, where θ is the angle between the axis of the polariser and the polarisation of the light - using a fairly simple argument which doesn't require too much maths.

Show the students that you can write an arbitrary polarisation as the sum of two polarisations, one parallel to the axis of the polariser and one perpendicular to it, using arrows (draw a right-angled triangle). Since the length of the side parallel to the axis is cos(θ) times the length of the hypotenuse, the amplitude is reduced by cos(θ). Intensity is amplitude squared (possibly use the analogy that kinetic energy depends on velocity squared), so the intensity is proportional to cos^2(θ).

If they're especially keen you can get them to sketch this. To explain why the curve is smooth and not pointy when it hits the x-axis, you could talk about x vs x^2.

## Birefringence

The box contains two pieces of card, with waves drawn on them, which slot together to form a model which can be used to demonstrate birefringence. By explaining that in certain materials one polarisation will travel slower than the other (possibly with reference to a drawing of a polymer structure, to explain why this happens), you can then demonstrate with the model that if one of these polarisations is shifted by half a wavelength the overall polarisation will rotate by 90°. You may need to explain that an arbitrary polarisation can be broken down into components parallel and perpendicular to the slow axis of the material.

You can then explain that, since the rotation depends on the second polarisation being shifted by a integer-plus-half multiple of the wavelength, only certain wavelengths of light will be transmitted through the second filter. This accounts for the colours observed - an extinction spectrum. You can use the Michel-Levy chart to show how the colour depends on the thickness of the material. The sellotape board is a good prop for explicitly showing this dependence, since the colours only change when pieces of tape cross over.

You can also expand on what sort of materials exhibit birefringence - typically these are materials with some sort of preferred direction, such as polymers in which the molecules are aligned in a certain direction (e.g. due to injection moulding - this can be seen in the pieces of ruler) or certain crystal structures.

The calcite is more strongly birefringent and thicker than the rulers: if you place the calcite over a line and look through it, you should see the line splitting into two (provided the calcite is clear enough!). This could be related to the difference in 'speed' between the two axes corresponding to a difference in refractive index. The difference in refractive index, through Snell's law, creates a difference in the angle of the light leaving the block, causing two images to be seen (Double Refraction).

## LCD Screen

The box contains a diagram of a twisted nematic structure (as found in a liquid crystal), as well as the construction of an LCD screen - use this to explain how it operates.

The liquid crystal molecules in the screen, under normal conditions, take the structure of a helix with a 90° twist from top to bottom. This will rotate polarised light passing through by the same angle. However, if a voltage is applied to the crystal, the molecules instead line up with the electric field, breaking the structure and preventing the rotation of polarised light. This causes a liquid crystal sample between crossed polars to go dark. This can then be exploited to build a display.

You could comment on how the screen uses ambient light, and not backlit, being energy efficient.

## Circular Polarisation

You can also use the model to demonstrate how circularly polarised light is possible - by shifting one of the pieces of card by 1/4 of a wavelength, you can show the the direction of polarisation rotates around as you move along the wave. Use this to explain how 3D glasses work, and ask them why it's beneficial to use circular polarisation and not linear polarisation in that scenario.

## Brewster's Angle

If there's time, and the conditions are right, you could comment on the Brewster Angle. At this angle unpolarised light incident on a reflective surface will be reflected with a plane of polarisation parallel to the surface. If there is a shiny horizontal surface (metal is best) in the area, you could ask them to look at it through a linear polariser (ideally polarising sunglasses if there are any to hand). With the polariser in a certain orientation, the glare should be greatly reduced. This is how glare reducing sunglasses work.