IB Physics How to Solve: IB Physics HL – Wave Phenomena (Young’s Double Slit, Thin-Film, Polarisation, Malus’ Law)

How to Solve: IB Physics HL – Wave Phenomena (Young’s Double Slit, Thin-Film, Polarisation, Malus’ Law)

Complete Guide

Introduction

Mastering wave phenomena unlocks 10–15% of your IB Physics HL Paper 2—and real-world tech like anti-glare sunglasses, fiber-optic internet, and medical imaging. One slip in path difference or phase shift, and you lose 4–6 marks on a single question. Let’s fix that.

WHAT YOU NEED TO KNOW FIRST

1. Superposition principle: When two waves meet, their displacements add.
2. Phase difference: Measured in radians or degrees; 360° = 2π rad = one full cycle.
3. Wavelength (λ): Distance between two consecutive crests (or troughs) in a wave.

KEY TERMS & FORMULAS

1. Young’s Double Slit (Interference)

Formula: MEMORISE THIS - Path difference (Δx) = d sinθ - d = slit separation (m) - θ = angle between central maximum and fringe (rad or °) - Fringe spacing (Δy) = λD / d - λ = wavelength (m) - D = distance from slits to screen (m) - d = slit separation (m)

Key Terms: - Constructive interference: Path difference = nλ (bright fringe) - Destructive interference: Path difference = (n + ½)λ (dark fringe) - Order (n): Integer (0, 1, 2, ...) for fringe number.

2. Thin-Film Interference

Formula: MEMORISE THIS - Phase shift on reflection: - 0° shift if wave reflects off lower refractive index medium. - 180° shift (π rad) if wave reflects off higher refractive index medium. - Condition for constructive interference: - 2tn = (m + ½)λ (if one phase shift occurs) - 2tn = mλ (if zero or two phase shifts occur) - t = film thickness (m) - n = refractive index of film - m = order (0, 1, 2, ...) - λ = wavelength in the film (λ = λ₀ / n, where λ₀ = vacuum wavelength)

Key Terms: - Optical path difference (OPD): 2tn (distance light travels in the film, adjusted for refractive index). - Phase shift: Sudden 180° change when reflecting off a denser medium.

3. Polarisation & Malus’ Law

Formula: MEMORISE THIS - Malus’ Law: I = I₀ cos²θ - I = transmitted intensity (W/m²) - I₀ = incident intensity (W/m²) - θ = angle between polariser and analyser (degrees or radians)

Key Terms: - Unpolarised light: Electric field oscillates in all directions perpendicular to propagation. - Plane-polarised light: Electric field oscillates in one plane. - Polariser: Device that transmits only one plane of polarisation. - Analyser: Second polariser used to measure intensity after first polariser.

STEP-BY-STEP METHOD

Young’s Double Slit (Interference)

Steps:
1. Identify given values: d (slit separation), D (screen distance), λ (wavelength), n (order).
2. Determine fringe type: Bright (constructive) or dark (destructive)?
3. Write path difference condition: - Bright: d sinθ = nλ - Dark: d sinθ = (n + ½)λ
4. Solve for θ (if needed).
5. Find fringe spacing (Δy) using Δy = λD / d (if question asks for distance between fringes).
6. Check units: Convert all to metres (m) and radians (rad) if necessary.

Thin-Film Interference

Steps:
1. Identify film properties: t (thickness), n (refractive index), λ₀ (vacuum wavelength).
2. Determine phase shifts: - Count reflections off higher n (180° shift each). - Total phase shifts: 0, 1, or 2.
3. Calculate wavelength in film: λ = λ₀ / n.
4. Write interference condition: - One phase shift: 2tn = (m + ½)λ (constructive) - Zero or two phase shifts: 2tn = mλ (constructive)
5. Solve for unknown (t, n, λ, or m).
6. Check for destructive interference (opposite conditions).

Polarisation & Malus’ Law

Steps:
1. Identify given values: I₀ (incident intensity), θ (angle between polarisers).
2. Apply Malus’ Law: I = I₀ cos²θ.
3. Solve for unknown (I, I₀, or θ).
4. Check units: θ must be in degrees or radians (calculator in correct mode).
5. For multiple polarisers: Apply Malus’ Law sequentially (intensity after first polariser becomes I₀ for the next).

WORKED EXAMPLES

Example 1 – Young’s Double Slit (Basic)

Question: Light of wavelength 600 nm passes through two slits separated by 0.2 mm. The screen is 1.5 m away. Find the distance between the 2nd and 3rd bright fringes.

Solution:
1. Given: λ = 600 × 10⁻⁹ m, d = 0.2 × 10⁻³ m, D = 1.5 m, n = 2 and n = 3.
2. Fringe spacing formula: Δy = λD / d.
3. Calculate Δy: Δy = (600 × 10⁻⁹ × 1.5) / (0.2 × 10⁻³) = 4.5 × 10⁻³ m = 4.5 mm.
4. Distance between 2nd and 3rd fringes = Δy = 4.5 mm.

What we did and why: We used the fringe spacing formula because the question asked for the distance between two adjacent bright fringes, not the position of a single fringe.

Example 2 – Thin-Film Interference (Medium)

Question: A soap film (n = 1.33) has a thickness of 300 nm. White light shines on it. What wavelength (in air) appears bright in the reflected light for m = 1?

Solution:
1. Given: t = 300 × 10⁻⁹ m, n = 1.33, m = 1.
2. Phase shifts: - Air (n = 1) → Film (n = 1.33): 1 phase shift (180°). - Film → Air: 0 phase shifts (reflects off lower n). - Total phase shifts = 1.
3. Constructive condition (1 phase shift): 2tn = (m + ½)λ.
4. Solve for λ (in film): 2 × 1.33 × 300 × 10⁻⁹ = (1 + ½)λ 798 × 10⁻⁹ = 1.5λ λ = 532 × 10⁻⁹ m (in film).
5. Convert to air wavelength: λ₀ = nλ = 1.33 × 532 × 10⁻⁹ = 708 nm.

What we did and why: We accounted for one phase shift (from air to film) and used the correct interference condition. Then, we converted the wavelength from the film to air because the question asked for the wavelength in air.

Example 3 – Malus’ Law (Exam-Style)

Question: Unpolarised light of intensity 8 W/m² passes through two polarisers. The first polariser is vertical. The second polariser is at 60° to the first. What is the final intensity?

Solution:
1. After first polariser (vertical): - Unpolarised light → polarised: I₁ = I₀ / 2 = 8 / 2 = 4 W/m².
2. After second polariser (60° to first): - Apply Malus’ Law: I₂ = I₁ cos²θ = 4 × cos²(60°). - cos(60°) = 0.5 → I₂ = 4 × (0.5)² = 4 × 0.25 = 1 W/m².

What we did and why: We halved the intensity after the first polariser (standard for unpolarised light) and then applied Malus’ Law sequentially for the second polariser.

COMMON MISTAKES

1. MISTAKE: Forgetting to convert nm to m in Young’s double slit. WHY IT HAPPENS: Students see "600 nm" and plug it directly into Δy = λD / d. CORRECT APPROACH: Always convert to metres (600 nm = 600 × 10⁻⁹ m).

2. MISTAKE: Ignoring phase shifts in thin-film interference. WHY IT HAPPENS: Students assume 2tn = mλ for all cases. CORRECT APPROACH: Count phase shifts first! One shift → (m + ½)λ, zero/two shifts → mλ.

3. MISTAKE: Using degrees in cos²θ without calculator mode. WHY IT HAPPENS: Students forget to set calculator to degrees (or radians). CORRECT APPROACH: Check calculator mode! cos(60°) ≠ cos(60 rad).

4. MISTAKE: Mixing up d (slit separation) and D (screen distance). WHY IT HAPPENS: Both are distances, but d is between slits, D is slits to screen. CORRECT APPROACH: Label the diagram: d = slit spacing, D = screen distance.

5. MISTAKE: Assuming all reflected light has a phase shift. WHY IT HAPPENS: Students think reflection always causes a 180° shift. CORRECT APPROACH: Only shift if reflecting off higher refractive index medium.

EXAM TRAPS

1. TRAP: "Wavelength in the film" vs. "wavelength in air." HOW TO SPOT IT: Question says "wavelength in air" but gives film thickness. HOW TO AVOID IT: Always convert λ₀ (air) to λ = λ₀ / n (film) before using interference conditions.

2. TRAP: Multiple polarisers with angles not relative to the first. HOW TO SPOT IT: Question says "second polariser is at 30° to the vertical" (not to the first polariser). HOW TO AVOID IT: Always measure θ relative to the previous polariser’s axis.

3. TRAP: "Dark fringe" in thin-film questions without phase shift check. HOW TO SPOT IT: Question asks for destructive interference but doesn’t specify phase shifts. HOW TO AVOID IT: Write the opposite condition of constructive interference (e.g., if constructive is 2tn = (m + ½)λ, destructive is 2tn = mλ).

1-MINUTE RECAP

"You’ve got this. Here’s the night-before cheat sheet:

1. Young’s double slit:
2. Bright fringes: d sinθ = nλ.
3. Fringe spacing: Δy = λD / d.

4. Convert nm to m!

5. Thin-film interference:

6. Count phase shifts (180° if reflecting off higher n).
7. One shift: 2tn = (m + ½)λ (constructive).
8. Zero/two shifts: 2tn = mλ (constructive).

9. Wavelength in film = λ₀ / n.

10. Polarisation:

11. Unpolarised → polarised: I = I₀ / 2.
12. Malus’ Law: I = I₀ cos²θ.
13. Calculator in degrees!

Common traps? Forgetting phase shifts, mixing up d and D, and not converting units. Double-check these, and you’ll nail it. Good luck!