The diffraction grating
Cambridge A-Level Physics (9702) · Unit 8: Superposition · 8 flashcards
The diffraction grating is topic 8.4 in the Cambridge A-Level Physics (9702) syllabus , positioned in Unit 8 — Superposition , alongside Stationary waves, Diffraction and Interference. In one line: The formula is d sin θ = nλ. This equation relates the grating spacing, angle to the maxima, the order number of the maximum, and the wavelength of the incident light.
Marked as AS Level: examined at AS Level in Paper 1 (Multiple Choice), Paper 2 (AS Structured Questions) and Paper 3 (Advanced Practical Skills). The same content may also be assumed in Paper 4 (A Level Structured Questions).
The deck below contains 8 flashcards — 2 definitions, 4 key concepts and 2 calculations — covering the precise wording mark schemes reward. Use the 2 definition cards to lock down command-word answers (define, state), then move on to the concept and calculation cards to handle explain, describe, calculate and compare questions.
Formula that relates the diffraction grating spacing (d), the angle to the nth order maximum (θ), the order number (n), and the wavelength of light (λ)
The formula is d sin θ = nλ. This equation relates the grating spacing, angle to the maxima, the order number of the maximum, and the wavelength of the incident light.
What the Cambridge 9702 syllabus says
Official 2025-2027 spec · AS LevelThese are the exact learning outcomes Cambridge sets for this topic. The candidate is expected to be able to do each of these on the relevant paper.
- recall and use d sin θ = nλ
- describe the use of a diffraction grating to determine the wavelength of light (the structure and use of the spectrometer are not included)
Cambridge syllabus keywords to use in your answers
These are the official Cambridge 9702 terms tagged to this section. Mark schemes credit responses that use the exact term — weave them into your answers verbatim rather than paraphrasing.
Tips to avoid common mistakes in The diffraction grating
- › Always use the relationship Intensity ∝ (Amplitude)² for any question involving the power or brightness of a wave.
- › In the equation d sinθ = nλ, always use the angle θ relative to the original path of the light.
- › Apply the condition for destructive interference: path difference equals (n + 1/2)λ. For a second-order dark fringe, the path difference is 3/2λ.
- › The principle of superposition states the resultant displacement is the sum of the individual displacements of the waves at that point.
- › In double-slit explanations, always state that waves must diffract at the slits to overlap and interfere.
State the formula that relates the diffraction grating spacing (d), the angle to the nth order maximum (θ), the order number (n), and the wavelength of light (λ).
The formula is d sin θ = nλ. This equation relates the grating spacing, angle to the maxima, the order number of the maximum, and the wavelength of the incident light.
What does 'd' represent in the formula d sin θ = nλ and what are its common units?
'd' represents the grating spacing, which is the distance between adjacent slits on the diffraction grating. It is commonly measured in meters (m), but can also be given in mm or μm. Ensure you convert to meters before using it in the formula.
Explain how a diffraction grating produces a series of bright fringes (maxima) when illuminated by monochromatic light.
A diffraction grating produces bright fringes due to the interference of light waves that have diffracted through the slits. Constructive interference occurs when the path difference between waves from adjacent slits is equal to an integer multiple of the wavelength (nλ), leading to bright fringes at specific angles.
A diffraction grating has 500 lines per mm. Calculate the grating spacing 'd'.
The grating spacing, d, is the inverse of the number of lines per unit length. d = 1 / (lines per unit length). Here, d = 1 / (500 lines/mm) = 1/(500 x 10^3 lines/m) = 2 x 10⁻⁶ m.
Describe how you would use a diffraction grating to determine the wavelength of monochromatic light.
Shine the light through the grating and measure the angle θ to a specific order maximum (n). Knowing the grating spacing (d) and order number (n), use the formula λ = d sin θ / n to calculate the wavelength λ.
Monochromatic light of wavelength 600 nm is incident on a grating with a spacing of 2.0 x 10⁻⁶ m. Calculate the angle of the first-order maximum.
Using d sin θ = nλ, rearrange to get sin θ = nλ / d. For the first order (n=1), sin θ = (1 * 600 x 10⁻⁹ m) / (2.0 x 10⁻⁶ m) = 0.3. Therefore, θ = arcsin(0.3) = 17.46 degrees.
What is the maximum number of orders of diffraction that can be observed for a given wavelength λ and grating spacing d?
The maximum number of orders is determined by the condition that sin θ ≤ 1. Therefore, n_max = d / λ, rounded down to the nearest whole number. If d/λ = 3.5, then a maximum of three orders can be observed either side of the zero order.
Why are diffraction gratings preferred over double slits for measuring the wavelength of light?
Diffraction gratings produce sharper and brighter fringes than double slits, making it easier to measure the angle θ accurately. The greater number of slits leads to increased intensity at the maxima and a more precise determination of wavelength.
Review the material
Read full revision notes on The diffraction grating — definitions, equations, common mistakes, and exam tips.
Read NotesMore topics in Unit 8 — Superposition
The diffraction grating sits alongside these A-Level Physics decks in the same syllabus unit. Each uses the same spaced-repetition system, so progress in one informs the next.
Key terms covered in this The diffraction grating deck
Every term below is defined in the flashcards above. Use the list as a quick recall test before your exam — if you can't define one of these in your own words, flip back to that card.
How to study this The diffraction grating deck
Start in Study Mode, attempt each card before flipping, then rate Hard, Okay or Easy. Cards you rate Hard come back within a day; cards you rate Easy push out to weeks. Your progress is saved in your browser, so come back daily for 5–10 minute reviews until every card reads Mastered.
Study Mode
Rate each card Hard, Okay, or Easy after flipping.