Polarisation (HSC SSCE Physics): Revision Notes

Polarisation

What is polarisation?

Polarisation is a phenomenon that distinguishes waves from streams of particles. It relates specifically to the direction in which the electric field oscillates in electromagnetic radiation.

In the wave model of light, electromagnetic radiation consists of oscillating electric and magnetic fields that are perpendicular to each other. These fields propagate at right angles to both field directions at the speed of light. Polarisation refers to the particular direction of oscillation of the electric field in the transverse plane.

Light from incandescent sources (like light bulbs or the Sun) contains particles vibrating in all directions at different speeds, so this light is described as unpolarised.

Historical context

French physicist Etienne Louis Malus pioneered the study of polarisation through his investigations of light reflecting from polished surfaces. His work established polarisation as a key characteristic of the wave nature of light.

Plane polarisation

Plane polarisation means that all the electric fields in the electromagnetic radiation are oscillating in the same two-dimensional plane. When this occurs, the light waves all vibrate in one particular direction.

There are several ways to convert unpolarised light into plane-polarised light:

• Reflection from surfaces
• Scattering
• Passing through a polarising filter

Polarisation by reflection

When light from an incandescent source (such as the Sun) reflects off a flat surface like a lake, the charged particles at the surface respond to the incoming light. Water, even at pH 7, contains some H⁺ and OH⁻ ions, while seawater contains additional ions. These ions can oscillate parallel to the surface but not perpendicular to it.

Here's what happens:

• Incoming light with the wrong orientation is scattered or absorbed
• Light oriented parallel to the surface causes the ions to oscillate
• These oscillating ions emit electromagnetic radiation
• All this emitted radiation is polarised parallel to the surface

Therefore, reflected sunlight is plane-polarised. This polarisation can be detected using an analyser - a device that only allows light of a particular polarisation to pass through.

Malus' Law

The wave model allows us to understand the relationship between the intensity of polarised light and the angle at which it passes through an analyser.

Intensity and amplitude

Deriving Malus' Law

Consider plane-polarised light with electric field amplitude $A_0$ passing through an analyser oriented at angle $\theta$ to the polarisation direction. The electric field vector can be broken down into two components:

• Component parallel to the analyser: $A_0 \cos\theta$
• Component perpendicular to the analyser: $A_0 \sin\theta$

Since the maximum intensity occurs when $\theta = 0$ (analyser parallel to polarisation), we can write:

$I = I_{\text{max}}\cos^2\theta$

This equation is known as Malus' Law. Note that $\cos^2\theta = (\cos\theta)^2$.

Understanding Malus' Law

Units of light intensity

The SI unit for light intensity is the lux. Light sources are often rated in lumen, which roughly represents the output of a candle. To account for distance and the inverse square law, we use the concept of flux - light output per unit area:

$1\text{ lux} = 1\text{ lumen} \cdot \text{m}^{-2}$

Investigation 10.5: Testing Malus' Law

Aim

To test the accuracy of Malus' Law

Materials

• Dissecting tray or other large, shallow, flat container
• Water
• Incandescent light source (desk lamp, light kit, or direct sunlight)
• Large sheet of cardboard (for shield)
• Scissors
• Plane polarising filter (analyser) - polarising plastic or sunglasses
• Stand/holder for analyser
• Diffraction grating mount
• Protractor
• Light meter or appropriate phone app

Risk assessment

Method

1. Set up the tray and almost fill it with water
2. Cut a slit in the cardboard shield and position it as shown in the diagram
3. Place the light meter in position and record a background light reading
4. Turn on the light source and record the light meter reading
5. Position the analyser between the shield and light meter
6. Record the light meter reading in a suitable table
7. Rotate the analyser by 10°
8. Repeat steps 6 and 7 until you have 18 readings

Results

Construct a table with the following columns:

1. Relative orientation of analyser
2. Measured light intensity
3. Adjusted values (subtract background light from step 3)
4. Angle $\theta$ relative to maximum intensity position
5. Calculated values using Malus' Law

Calculate expected values using Malus' Law: $I = I_{\text{max}}\cos^2\theta$

Plot both your measured results (column 3) and calculated values (column 5) against the angle of rotation on the same graph.

Analysis of results

1. Comment on the accuracy of your measurements and estimate the error
2. Compare the plot of measured results with expected results
3. Evaluate the reliability and validity of your results
4. Identify any deficiencies and suggest improvements

Conclusion

Discuss whether the investigation met its aim. How well do your results agree with Malus' Law predictions? Since Malus' Law derives from the wave model of light, does your experimental evidence support this model?

Investigation 10.6: Monochromatic light and Malus' Law

Aim

To determine whether monochromatic light obeys Malus' Law

Additional materials

• Materials from Investigation 10.5
• Red, green, and blue filters

Method

1. Place a red filter between the light source and polariser (water tray)
2. Repeat steps 3-7 from Investigation 10.5
3. Repeat for green and blue filters

Analysis

Compare results for different colours with those from Investigation 10.5. Examine whether:

• $I_{\text{max}}$ differs between individual colours
• Coloured filters significantly affect the relationship predicted by Malus' Law
• The wave model remains valid for monochromatic light

Remember!