MYP Physics · topic MYP-09.04
Diffraction and grating evidence
Connect the ideas, make your working visible, and test the result. Use the hints when you need a starting point; open the full solution after your attempt.
Extra challenging questions
Work through the linked stages and explain what each result means.
A diffraction grating with an impossible order
Optional enrichment: this challenge may extend beyond the usual syllabus depth and assumes confidence with algebra and graph interpretation. 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]
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.
Show a hint
Begin with part (a): Find grating spacing, wavelength, frequency and the largest possible order.
Reveal the worked solution
- 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.
Answer (a) d = 2.0 μm; λ = 600 nm; f = 5.0×10¹⁴ Hz; maximum order = 3. (b) Diffraction spreads each slit contribution; interference between the many coherent slit contributions selects the narrow orders.
Compare the assumptions, method and units with your attempt. Explain any correction before trying another question.