Physics • Year 12 • Module 7 • Lesson 3
Interference — Young’s Double Slit
Build HSC Band 5–6 extended-response technique on evaluating interference evidence, designing investigations, and arguing from historical data.
1. Data + scenario: Young’s 1801 double slit experiment (Band 5–6)
8 marks Band 5–6
Scenario. In 1801, Thomas Young directed sunlight through a narrow single slit and then through two closely-spaced parallel slits (separation d ≈ 0.3 mm) onto a screen placed L ≈ 3 m away. He reported observing “a number of alternate dark and bright stripes.” He measured the fringe spacing to be approximately 4.4 mm. Before this experiment, Newton’s corpuscular (particle) theory of light was the dominant model; it predicted that particles passing through two slits would form two bright patches on the screen.
| Measurement / observation | Young’s data |
|---|---|
| Slit separation d | 0.3 mm |
| Slit-to-screen distance L | 3.0 m |
| Measured fringe spacing Δx | 4.4 mm |
| Pattern observed | Multiple alternating bright and dark fringes |
| Effect of covering one slit | Alternating pattern vanished; single wide bright band remained |
Illustrative data based on Young, T. (1804). Philosophical Transactions of the Royal Society, 94, 1–16.
Q1. Analyse and evaluate Young’s experimental data to assess the evidence for the wave nature of light. In your response you must:
- Use the data to calculate the wavelength of sunlight implied by Young’s measurement and state what colour of visible light this corresponds to.
- Explain why the observation of multiple alternating fringes is inconsistent with the particle model and consistent with the wave model, referring to superposition.
- Analyse the significance of Young’s observation when one slit was covered, and explain what this result demonstrates about the role of the two-slit geometry.
- Evaluate one limitation of Young’s experimental design (using sunlight rather than a laser) and explain how it affects the quality of the interference pattern.
- State one way Young’s experiment could be improved using modern technology.
2. Experimental design — determining an unknown wavelength in the school lab (Band 5–6)
7 marks Band 5–6
Research question. A student has been given an unmarked low-power laser pointer of unknown wavelength (estimated to be somewhere in the visible range, 400–700 nm). Design a double slit experiment to accurately determine the wavelength of this laser using standard school laboratory equipment.
Constraints: Available equipment: the unknown laser, a double slit slide (d = 0.25 mm), a metre ruler, a measuring tape, a screen (white cardboard), and a vernier calliper or digital calliper (resolution 0.02 mm). The experiment must be completed in one 45-minute lesson.
Q2. Design the investigation and present it in the format below.
- State your hypothesis, including the formula you will use to calculate λ.
- 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 improve accuracy in measuring fringe spacing.
- Explain what result would indicate your measurement is unreliable.
- State two sources of uncertainty and explain which is likely to be the dominant source of error.
Q1 — Sample Band 6 response (8 marks), annotated
Wavelength calculation: Using λ = Δx × d / L = (4.4×10−3 m × 0.3×10−3 m) / 3.0 m = 4.4×10−7 m = 440 nm. This is in the violet region of the visible spectrum (380–450 nm). [1 mark for correct calculation; 1 mark for correct colour identification]
Wave vs particle model: The particle (corpuscular) model predicts that particles travelling through two slits follow straight-line paths and land in two distinct patches behind each slit — no mechanism exists for particles to cancel and produce dark regions between the bright patches. The wave model predicts that waves from the two slits overlap and superpose: where crests from both slits arrive simultaneously (path difference = nλ), constructive interference produces a bright fringe; where a crest from one slit meets a trough from the other (path difference = (n + ½)λ), destructive interference produces a dark fringe. The multiple alternating fringe pattern observed is the hallmark of superposition and is fundamentally inexplicable by the particle model. [1 mark for explaining particle model failure; 1 mark for correct superposition/wave explanation with constructive and destructive interference]
One slit covered: When one slit was covered, the alternating pattern disappeared and was replaced by a single wide bright band. This demonstrates that the interference pattern requires two coherent sources: when only one slit is open, there is no second source to interfere with, so superposition cannot occur. The single broad band is due to single-slit diffraction. This observation also rules out the possibility that the fringes arose from imperfections in the slits rather than wave interference. [1 mark for correct explanation of what disappeared and why; 1 mark for explicitly stating that two sources are required for interference]
Limitation of sunlight: Sunlight is a mixture of all visible wavelengths (it is not monochromatic). Each wavelength produces its own fringe pattern with its own spacing (Δx = λL/d), and these overlapping patterns blur the fringes together, making them difficult to see clearly — especially for higher-order fringes. This reduces the precision of Young’s fringe-spacing measurement and thus the precision of his derived wavelength. [1 mark for identifying non-monochromatic nature of sunlight as the limitation; 1 mark for explaining how overlapping patterns reduce fringe clarity]
Modern improvement: Using a monochromatic, coherent laser source instead of sunlight would produce sharp, well-defined fringes of a single wavelength, greatly improving the precision of the measurement. [½ mark — accept any valid improvement: e.g. use a diffraction grating for higher resolution; use a CCD detector for precise fringe position measurement]
Marking criteria summary (8 marks): 1 = correct calculation of λ using Δx = λL/d (must show rearrangement and unit conversion); 1 = correct colour identification (violet, 440 nm); 1 = explains why particle model fails (no cancellation mechanism); 1 = explains wave model via superposition / constructive and destructive interference; 1 = correctly interprets one-slit result (two sources required); 1 = links to removal of interference (not single-slit diffraction confusion); 1 = identifies limitation (non-monochromatic sunlight blurs fringes); 1 = suggests valid modern improvement.
Q2 — Sample Band 6 response (7 marks), annotated
Hypothesis: If the wavelength of the laser can be determined by measuring the fringe spacing Δx in a double slit experiment, then using λ = Δx × d / L with known d = 0.25 mm and measured L and Δx will yield the wavelength. Independent variable: slit-to-screen distance L (varied to check consistency). Dependent variable: fringe spacing Δx. Controlled variables: slit separation d (fixed at 0.25 mm); room lighting (dim to improve contrast); orientation of slit slide (perpendicular to beam). [1 mark for hypothesis with formula; 1 mark for IV and DV identified; 0.5 mark per controlled variable up to 1 mark]
Procedure: (1) Set up the laser on a bench pointing horizontally at the white screen. Insert the double slit slide (d = 0.25 mm) between the laser and the screen. Darken the room. (2) Measure and record the slit-to-screen distance L with the measuring tape to the nearest 5 mm; use L ≈ 1.5 m initially. (3) Observe the interference pattern on the screen. Use the digital calliper to measure the total width W across n = 10 consecutive bright fringe centres (i.e. the distance from fringe 1 to fringe 11). Divide W by 10 to obtain Δx. Record three separate measurements of W and calculate the mean. (4) Repeat steps 2–3 for L = 2.0 m and L = 2.5 m. Calculate λ = Δx × d / L for each L setting and determine the mean wavelength. [1 mark for four steps; 1 mark for the n-fringe averaging technique specifically mentioned]
Unreliable result: If the three values of λ calculated at different L values differ by more than ∼20 nm, the measurement is unreliable — this suggests the fringe spacing was poorly measured (possibly due to vibration, blurring, or the laser not being perpendicular to the slit slide). [1 mark]
Sources of uncertainty: (1) Measurement of Δx using a ruler or calliper — even with the n-fringe method, fringe edges are not perfectly sharp due to diffraction broadening, introducing a reading uncertainty of ~0.1 mm in W. (2) Measurement of the slit-to-screen distance L with a measuring tape — typically ±5 mm over 1.5 m. The dominant source of error is the fringe spacing measurement, because Δx is only a few millimetres and even a 0.1 mm error represents ~2–5% relative uncertainty, whereas the 5 mm error in L = 1.5 m represents only ~0.3% relative uncertainty. [1 mark for two sources; 1 mark for identifying Δx measurement as dominant with relative uncertainty reasoning]
Marking criteria summary (7 marks): 1 = hypothesis with λ = Δx × d / L formula and IV/DV; 1 = at least two controlled variables; 1 = four clear steps; 1 = n-fringe averaging technique to improve accuracy; 1 = criterion for unreliable result (consistency across L values); 1 = two valid sources of uncertainty; 1 = identifies dominant source with quantitative or comparative justification.