Physics • Year 12 • Module 7 • Lesson 5
Polarisation of Light
Build HSC Band 5–6 extended-response technique on polarisation, Malus’s Law, multi-polariser chains, and evaluating the wave nature of light.
1. Multi-polariser chain analysis (Band 5–6)
8 marks Band 5–6
Scenario. A photonics engineer is testing the polarisation control system for an LCD display prototype. She passes unpolarised laser light of intensity I0 = 480 W/m² through a sequence of four polarising filters: P1 (vertical axis), P2 (at 30° to P1), P3 (at 30° to P2), and P4 (at 30° to P3). She records the intensity after each filter. She then removes P2 and P3, leaving only P1 and P4 in the beam path.
Q1. Analyse the polarisation system described above. In your response you must:
- Calculate the transmitted intensity after each of the four polarisers in the complete chain. Show all working using Malus’s Law.
- Calculate the transmitted intensity through P1 and P4 only (after removing P2 and P3). Show your working.
- Compare the two final intensities and explain the physical reason why the result with intermediate polarisers differs from the result without them.
- State one practical advantage of using a chain of intermediate polarisers rather than a single large-angle rotation in an LCD control system.
2. Experimental design — verifying Malus’s Law in the lab (Band 5–6)
7 marks Band 5–6
Research question. A student claims that Malus’s Law (I = I0 cos2 θ) is only approximately true, and that the real relationship is linear (I ∝ cos θ, not cos2 θ). Design a laboratory investigation to test which relationship correctly describes how the intensity of polarised light changes as an analyser is rotated from 0° to 90°.
Constraints: You have access to a laser pointer (plane-polarised output), a rotatable polarising filter (acting as analyser), a light intensity meter (in W/m²), a protractor, a retort stand, and a digital logger. The investigation must be completable in a single 75-minute practical session.
Q2. Design the investigation and present it in the format below.
- State a clear, testable hypothesis that distinguishes between the linear and cosine-squared relationships.
- Identify the independent variable, dependent variable, and at least two controlled variables.
- Describe the procedure in at least four numbered steps, including how you will record data to distinguish between the two relationships.
- Explain how you will process and graph the data to determine which relationship is correct.
- State two sources of error and one improvement to address them.
Q1 — Sample Band 6 response (8 marks), annotated
Four-polariser chain (4 marks):
After P1 (polariser from unpolarised light): I1 = I0/2 = 480/2 = 240 W/m² [1]. Light is now vertically plane-polarised.
After P2 (30° to P1): I2 = 240 × cos2 30° = 240 × 0.75 = 180 W/m² [1].
After P3 (30° to P2): I3 = 180 × cos2 30° = 180 × 0.75 = 135 W/m² [1].
After P4 (30° to P3): I4 = 135 × cos2 30° = 135 × 0.75 = 101.25 W/m² ≈ 101 W/m² [1].
P1 and P4 only (1 mark): P4 is at a total angle of 3 × 30° = 90° from P1. Applying Malus’s Law: I = 240 × cos2 90° = 240 × 0 = 0 W/m² [1]. No light is transmitted.
Comparison and physical reason (2 marks): With the intermediate polarisers P2 and P3, the final intensity (~101 W/m²) is much greater than zero; without them, the intensity is zero [1]. The physical reason is that each intermediate polariser re-polarises the light at a new angle. After P2, the light is polarised at 30° from vertical; after P3, at 60°. When this 60°-polarised light hits P4 (which is at 30° to P3, i.e. 90° from P1 but only 30° from P3), the relevant angle for Malus’s Law is 30°, not 90°. Without the intermediate filters, the polarised beam from P1 (vertical) hits P4 directly at 90°, so cos2 90° = 0 and all light is blocked [1].
Practical advantage (1 mark): Using a chain of small-angle rotations allows fine, graduated control of transmitted intensity; a single large-angle jump (e.g. 0° to 90°) gives binary on/off behaviour, whereas multiple intermediate steps allow analogue dimming of each pixel in the LCD display [1].
Marking criteria summary (8 marks): 1 per correct intensity (4 marks); 1 = correct P1+P4 result (zero, with reasoning that 90° total); 1 = identifies that the intermediate polarisers prevent direct 90° cancellation; 1 = explains re-polarisation mechanism at each step; 1 = states a valid practical advantage linked to intensity control or LCD operation.
Q2 — Sample Band 6 response (7 marks), annotated
Hypothesis: If Malus’s Law (I = I0 cos2 θ) is the correct relationship, then a plot of transmitted intensity I vs cos2 θ will yield a straight line through the origin with gradient I0; a plot of I vs cos θ will be a curve (non-linear). IV: analyser angle θ. DV: transmitted intensity I. Controlled variables: incident intensity (keep laser output constant), distance from laser to meter, ambient light level (darken room). [1]
Procedure: (1) Set up the laser on a retort stand directed at the intensity meter; ensure the laser output is already plane-polarised (check with a separate polariser — if rotating it varies the intensity, the laser is polarised). Set the analyser at 0° and record I0. (2) Rotate the analyser in 10° increments from 0° to 90°. At each angle, record the intensity reading from the digital logger when stable. Record angle and intensity in a results table. (3) For each reading, calculate cos θ and cos2 θ. (4) Plot two graphs on separate axes: (a) I vs cos2 θ and (b) I vs cos θ. [1]
Data processing: If graph (a) is a straight line through the origin (R2 ≈ 1 for a linear fit), Malus’s Law is verified. If graph (b) is non-linear (curved), the linear hypothesis is rejected. The gradient of graph (a) gives the incident intensity I0, which can be checked against the direct measurement at 0°. [1]
Falsification: If graph (a) is non-linear but graph (b) is a straight line, the data would falsify Malus’s Law and support the linear relationship. [1]
Sources of error: (1) Parallax when reading the protractor angle, causing systematic error in θ and therefore in cos2 θ values [1]. (2) Ambient (background) light contributing to intensity meter readings, inflating all I values and distorting the shape of both graphs [1].
Improvement: Conduct the experiment in a darkened room or use a light-tight enclosure around the beam path, and take three repeat readings at each angle and use the mean to reduce random error [1].
Marking criteria summary (7 marks): 1 = testable hypothesis stating how to distinguish the two relationships graphically; 1 = four clear procedure steps including data table and two graph plots; 1 = data processing method (identifying straight-line graph for cos2 θ); 1 = states what result would falsify the hypothesis; 1 = valid source of error 1 (parallax or angle reading); 1 = valid source of error 2 (ambient light or laser fluctuation); 1 = specific improvement addressing at least one error with clear reasoning.