AQA AS Level Physics Paper 2, June 2025: Question 1

✅ Acceptable Precautions (Any one)

• Stand behind the laser when it is switched on.
• Avoid looking directly down the beam or at specular reflections.
• Put up a laser warning sign outside/inside the room.
• Turn the laser off when not actively in use.
• Ensure the laser is securely clamped to prevent accidental movement.
• Operate the laser above or below normal eye level.
• Wear laser safety goggles/glasses (specific to wavelength).

❌ Common Rejections

• "Wear safety goggles": Insufficient. Standard workshop or chemistry splash goggles provide zero laser protection. You must specify laser safety goggles.
• "Don't shine it into someone's eyes": Rejected. This is treated as common sense/poor conduct rather than a formal laboratory safety precaution.

📐 Step-by-Step Calculation

Step 1: Identify the second-order spot

• Spot C is the central maximum (n = 0) at x = 553 mm.
• Spot B is adjacent on the left (553 − 321 = 232 mm) → n = 1.
• Spot D is adjacent on the right (785 − 553 = 232 mm) → n = 1.
• Spot A is the second fringe to the left → n = 2.

Δx = x_C − x_A = 553 − 60 = 493 mm

Step 2: Calculate percentage uncertainty

• Both positions have an absolute uncertainty of ±5 mm.
• When subtracting values, absolute uncertainties add:
  Absolute uncertainty = 5 mm + 5 mm = 10 mm
• Percentage uncertainty = (10 / 493) × 100% = 2.0%

🧠 Exam Technique & Traps

• Adding uncertainties: Never subtract uncertainties! When values are subtracted (x_C − x_A), their absolute uncertainties always add together.
• Significant figures: Percentage uncertainties should usually be quoted to 1 or 2 significant figures (e.g., 2% or 2.0%). Quoting 2.028% will lose marks if the examiner enforces the 1–2 s.f. rule.
• Show full working: Both marks require visible evidence of your method.

📐 Full Step-by-Step Method

Step 1: Calculate the slit separation (d)

Grating = 300 lines mm⁻¹ = 300 000 lines m⁻¹
d = 10⁻³ / 300 = 3.33 × 10⁻⁶ m

Step 2: Determine angle θ accurately

Distance to screen D = 1.20 m.

Using n = 1 (Spot B or D, Δx = 0.232 m):

tan θ₁ = 0.232 / 1.20 = 0.1933 → θ₁ = 10.94°
sin θ₁ = sin(10.94°) = 0.190

Using n = 2 (Spot A, Δx = 0.493 m):

tan θ₂ = 0.493 / 1.20 = 0.4108 → θ₂ = 22.33°
sin θ₂ = sin(22.33°) = 0.380

Step 3: Solve for wavelength (λ)

λ = (d sin θ) / n
λ₁ = (3.33 × 10⁻⁶ × 0.190) / 1 = 6.33 × 10⁻⁷ m
λ₂ = (3.33 × 10⁻⁶ × 0.380) / 2 = 6.33 × 10⁻⁷ m

Final Answer: 6.3 × 10⁻⁷ m (or within 6.2 × 10⁻⁷ to 6.4 × 10⁻⁷ m)

📐 Step-by-Step Calculation

Step 1: Read the new position from Figure 2

• Grid squares are 50 mm × 50 mm.
• Central maximum C is in the middle.
• Counting squares from C to B (or C to D): exactly 8 grid squares.
• New fringe spacing Δx_new = 8 × 50 mm = 400 mm = 0.400 m.

Step 2: Calculate new screen distance (L)

Method A — Using the diffraction angle (tan θ):

Since the laser wavelength and grating spacing are unchanged, the diffraction angle for the first order remains θ₁ (where tan θ₁ = 0.1933):

tan θ₁ = Δx_new / L
L = 0.400 / tan(10.94°) = 0.400 / 0.1933 = 2.07 m

Method B — Using similar triangles:

L / L_original = Δx_new / Δx_original
L = 1.20 × (0.400 / 0.232) = 2.07 m

Rounds to: 2.1 m

🧠 Examiner Insight

• Read scale indicators: The scale at the bottom of Figure 2 clearly specifies each grid square is 50 mm wide. Count carefully from C to the edge spots.
• Consistency of angles: The angle θ depends only on the grating and the wavelength. Moving the screen does not change θ, only the projected distance on the screen.
• Mark dependency: Mark 2 (the final numerical answer of 2.1 m) is dependent on having a valid physical method in Mark 1.