CP6 – Diffraction Grating | Edexcel A Level Physics

Theory & Background

Diffraction gratings, the grating equation and measuring wavelength

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Laser Safety: Never look directly into a laser beam or its reflections. Do not point the laser at other people. Place a beam stop behind the grating. The simulation uses a safe virtual laser — in the real experiment always follow your school's laser safety protocol and wear appropriate eye protection.

Objectives

Use a diffraction grating to produce an interference pattern from a laser or white light source
Measure the angles of diffraction for orders n = 1, 2, 3 and apply nλ = d sinθ
Plot n against sinθ — gradient = d/λ — to determine the wavelength λ
Compare results using screen distance and direct angle methods

The Diffraction Grating Equation

A diffraction grating has many equally spaced slits. When light passes through, each slit acts as a point source of secondary wavelets (Huygens' construction). Constructive interference occurs at angles where the path difference between adjacent slits equals a whole number of wavelengths:

nλ = d sinθ

n = order number (integer: 0, ±1, ±2, …)
λ = wavelength of light (m)
d = slit spacing = 1/N where N = number of lines per metre
θ = angle of diffraction from the straight-through (zeroth order)

Rearranging: sinθ = nλ/d. So a graph of sinθ (y-axis) against n (x-axis) gives a straight line through the origin with gradient λ/d. Since d is known from the grating specification: λ = gradient × d.

Slit Spacing d

Gratings are specified by the number of lines per millimetre (lines/mm). The slit spacing d is:

d = 1 / N (in metres, where N is lines per metre) e.g. 300 lines/mm → N = 300,000 lines/m → d = 1/300,000 = 3.33 × 10⁻⁶ m

Two Measurement Methods

Screen distance method: Place a screen at distance D from the grating. Measure the distance y from the central maximum to the nth order maximum. Then tanθ = y/D, so θ = arctan(y/D). For small angles, sinθ ≈ tanθ ≈ y/D.

Direct angle method: Use a protractor or optical bench to measure the angle θ directly. More precise — avoids the approximation error at larger angles.

Screen method: tanθ = y/D → θ = arctan(y/D) Direct method: read θ from protractor or angle scale

Use direct angle method when θ > 20° — the small angle approximation breaks down significantly beyond this point.

Laser vs White Light

Laser: Monochromatic (single wavelength), coherent, very bright. Produces sharp, bright maxima at precise angles. Ideal for measurement.

White light: Contains all visible wavelengths (~400–700 nm). Each wavelength diffracts at a different angle, producing a continuous spectrum in each order. Violet diffracts least (smallest θ), red diffracts most. The zeroth order (n = 0) is always white.

Step-by-Step Procedure

Select your measurement method — procedure updates to match.

Method:

Light Source

Laser wavelength λ 532 nm

380 nm (violet)700 nm (red)

Diffraction Grating

Measurement Method

Screen distance D 1.00 m

0.50 m2.00 m

Diffraction order n n = 1

Angle θ

—

sinθ

—

y (screen)

—

Calc. λ

—

Readings recorded: 0 / 3 minimum

Screen view — drag to measure fringe position

Results Data Table

Auto-filled from simulation. λ calculated from each reading using nλ = d sinθ.

#	Grating lines/mm	n	Method	y / mm	D / m	θ / °	sinθ	d / nm	λ = d sinθ/n / nm
No data yet — go to Simulation tab.

Graph & Analysis

Plot sinθ (y-axis) against n (x-axis). Gradient = λ/d → λ = gradient × d.

Uncertainty Estimate

Select an investigation to see uncertainty estimates.

Discussion Questions

Write your answers and reveal model answers when ready.

Question 1

Explain why the diffraction grating produces a series of bright maxima at specific angles. Use path difference in your answer.

Each slit in the grating acts as a point source of secondary wavelets (Huygens' principle). For constructive interference to occur at angle θ, the path difference between adjacent slits must equal a whole number of wavelengths: path difference = d sinθ = nλ. At this angle, all waves from all slits arrive in phase and interfere constructively, producing a bright maximum (the nth order). At any other angle, contributions from different slits partially cancel, giving much lower intensity.

Question 2

A student uses a 600 lines/mm grating with a green laser (λ = 532 nm). Calculate the angle of the second-order maximum and state whether a third-order maximum exists.

d = 1/(600×10³) = 1.667×10⁻⁶ m. For n=2: sinθ = nλ/d = (2 × 532×10⁻⁹)/(1.667×10⁻⁶) = 1.064×10⁻⁶/1.667×10⁻⁶ = 0.6383. θ = arcsin(0.6383) = 39.6°. For n=3: sinθ = 3×532×10⁻⁹/1.667×10⁻⁶ = 0.957, θ = 73.2°. Since sinθ < 1, the 3rd order exists at 73.2°. For n=4: sinθ = 4×532/1667 = 1.276 > 1 — impossible. So the maximum observable order is n=3.

Question 3

Explain why the graph of sinθ against n should be a straight line through the origin. What does the gradient represent?

From nλ = d sinθ, rearranging: sinθ = (λ/d) × n. This is of the form y = mx where y = sinθ, x = n, and m = λ/d is constant (since λ and d are both fixed). Therefore sinθ is directly proportional to n — a straight line through the origin. The gradient m = λ/d, so the wavelength is found by: λ = gradient × d. The graph passes through the origin because when n = 0 (the central maximum), θ = 0 and sinθ = 0.

Question 4

Explain why white light produces a spectrum in each diffraction order, and why the zeroth order is always white.

White light contains all wavelengths from approximately 400 nm (violet) to 700 nm (red). From nλ = d sinθ, for a given order n, different wavelengths diffracts to different angles: violet (smallest λ) diffracts to the smallest angle, red (largest λ) to the largest. This separation produces a continuous spectrum in each order. The zeroth order (n=0) is always white because sinθ = 0 regardless of wavelength — all wavelengths travel straight through without being dispersed, so they all arrive at the same central position and recombine to give white light.

Question 5

Suggest two sources of uncertainty specific to this experiment and explain how each could be reduced.

1. Difficulty measuring y accurately — the diffraction maxima may not be perfectly sharp, making it hard to identify the centre of each fringe precisely. This introduces uncertainty in y and therefore in θ and λ. Reduce by: measuring from the left-side maximum to the right-side maximum of the same order (measuring 2y) and dividing by 2 — this averages out any asymmetry and doubles the measurement, reducing percentage uncertainty. 2. Grating not perpendicular to the incident beam — if the grating is tilted, the measured angle is incorrect for the geometry assumed in nλ = d sinθ. This introduces a systematic error. Reduce by: using an optical bench with a precision mount, checking that the zeroth order is exactly straight-through, and rotating the grating until the +n and −n orders are equidistant from the central maximum.