AP · AP 2 · extended response
A diffraction grating with an impossible order
AP Physics 2: Algebra-Based · Original GioPhysics question with a detailed, mark-by-mark answer guide.
- Demand
- discriminating
- Marks
- 6
- Topics
- 1
- Answer
- Complete
Diffraction orders
Supplied question data. Read the labelled axes and use the observations to test the physical model.
Vertical axis (y): sin θ
Horizontal axis (x): Order n
Read the exact data as a table
| Order n | sin θ |
|---|---|
| 0 | 0 |
| 1 | 0.3 |
| 2 | 0.6 |
| 3 | 0.9 |
These are the supplied values, not a worked answer. No fitted trend is drawn.
Choose your AP course · School year 2026–27 · May 2027 exam
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Choose reviewed AP practice →Monochromatic light falls normally on a grating with 500 lines per millimetre. Measured sine of the diffraction angle against order is supplied below. Use c = 3.0×10⁸ m s⁻¹. Angles are measured from the central direction, not from the grating surface. Supplied model: Use d sinθ = nλ and spacing d = 1/(lines per unit length). Supplied data (Order n; sin θ): (0, 0), (1, 0.3), (2, 0.6), (3, 0.9).
- (a)
Find grating spacing, wavelength, frequency and the largest possible order.
3 marks - (b)
Explain how to distinguish an aperture's diffraction envelope from the grating's narrow interference maxima, and improve an angle measurement.
3 marks
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(a)
Find grating spacing, wavelength, frequency and the largest possible order.
Build a chain of claim, evidence and physics reasoning. Address more than one relevant factor, identify a limitation or assumption, and finish with a conclusion that is conditional on the evidence rather than absolute.
- 1
500 lines mm⁻¹ is 5.0×10⁵ lines m⁻¹, so d = 1/(5.0×10⁵) = 2.0×10⁻⁶ m.
- 2
From d sinθ = nλ, λ/d is the graph gradient, 0.30; therefore λ = 6.0×10⁻⁷ m and f = c/λ = 5.0×10¹⁴ Hz.
- 3
The condition sinθ≤1 requires n≤d/λ = 3.33. Integer orders stop at n = 3; a fourth order would require sinθ = 1.2.
(b)
Explain how to distinguish an aperture's diffraction envelope from the grating's narrow interference maxima, and improve an angle measurement.
Build a chain of claim, evidence and physics reasoning. Address more than one relevant factor, identify a limitation or assumption, and finish with a conclusion that is conditional on the evidence rather than absolute.
- 1
The grating equation predicts directions of principal maxima, while finite slit width determines their broad intensity envelope.
- 2
Measure both +n and −n peaks; half their angular separation reduces an offset in the estimated central direction.
- 3
Repeat and use higher visible orders where practical, while avoiding weak peaks and confusion between order number and wavelength. Never view a laser directly.
Complete marking guidance
Use these worked steps alongside the part-by-part answers. They explain the method and mark allocation; they do not add extra marks.
- 500 lines mm⁻¹ is 5.0×10⁵ lines m⁻¹, so d = 1/(5.0×10⁵) = 2.0×10⁻⁶ m.
- From d sinθ = nλ, λ/d is the graph gradient, 0.30; therefore λ = 6.0×10⁻⁷ m and f = c/λ = 5.0×10¹⁴ Hz.
- The condition sinθ≤1 requires n≤d/λ = 3.33. Integer orders stop at n = 3; a fourth order would require sinθ = 1.2.
- The grating equation predicts directions of principal maxima, while finite slit width determines their broad intensity envelope.
- Measure both +n and −n peaks; half their angular separation reduces an offset in the estimated central direction.
- Repeat and use higher visible orders where practical, while avoiding weak peaks and confusion between order number and wavelength. Never view a laser directly.
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