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TL;DR A diffraction grating splits light into sharp, bright orders because hundreds of parallel slits interfere constructively at specific angles. Shine a laser through the grating, measure the distance from the central maximum to the first-order spot, and use dsinθ=nλ to calculate the wavelength. For multi-order data, plot sinθ against n - the gradient gives λ/d. A CD works as a crude grating too: the rainbow you see is diffraction from its spiral track.
When a wave passes through an opening (or past an edge) whose size is comparable to its wavelength, the wave spreads out. This spreading is called diffraction. You can see it when water waves pass through a harbour gap or when sound bends around a doorway.
For light, individual slits are too narrow to see with the eye, but the effects are measurable. A single narrow slit produces a broad diffraction pattern. The real power comes when you line up many slits side by side - that is a diffraction grating.
What Is a Diffraction Grating?
A diffraction grating is a flat surface ruled with hundreds or thousands of equally spaced parallel slits per millimetre. Each slit acts as a separate source of coherent waves (assuming the incident light is coherent, such as laser light). Because the slits are evenly spaced, the secondary wavelets from adjacent slits interfere constructively only at certain well-defined angles, producing sharp, bright maxima called orders.
The condition for constructive interference is:
dsinθ=nλ
where:
d = slit spacing (distance between adjacent slits), in metres
θ = angle between the central maximum and the n-th order maximum
n = order number (0, 1, 2, 3, ...)
λ = wavelength of the light, in metres
A grating labelled "600 lines/mm" has N=600 lines per millimetre. The slit spacing is d=1/N. For 600 lines/mm:
d=6000001m=1.667×10−6m
This equation and conversion are central to the experiment. Make sure you are comfortable going from lines/mm to d in metres before you start.
Apparatus
You will need:
Laser pointer (Class 2, below 1 mW) or a ray box with a single-colour filter
Diffraction grating with a known number of lines per mm (300 or 600 lines/mm are common in schools)
Metre ruler (resolution 1 mm)
Screen or plain white wall
Retort stand, boss, and clamp (to hold the grating steady)
Tape measure (for the grating-to-screen distance D)
Pencil and adhesive tape (to mark spot positions on the screen)
Protractor or trigonometric measurement setup (ruler + calculator is usually better)
Safety note: Never look directly into the laser beam. Keep the beam at bench height and below eye level. A Class 2 laser pointer (below 1 mW) is safe for classroom use provided students do not stare into the beam. If using a ray box, the colour filter selects a narrow band of wavelengths to approximate monochromatic light.
Step-by-Step Method
1. Set up the laser and grating
Clamp the diffraction grating vertically on the retort stand. Position the laser so its beam hits the grating perpendicularly (at 90 degrees to the grating surface). Place a white screen or wall 1.0 m to 2.0 m away from the grating. The greater the distance D, the larger the separation between orders, making measurements easier.
2. Identify the maxima
Switch on the laser. You should see a bright central maximum (the zero-order, n=0) directly ahead, with symmetric bright spots on either side. The first spots on each side are the first-order maxima (n=1). Further out you may see second-order (n=2) and possibly third-order spots.
3. Measure the grating-to-screen distance D
Use the tape measure to record the perpendicular distance from the grating to the screen. Measure in metres. A typical value is D=1.000 m.
4. Measure the distance x from the central maximum to each order
Use the metre ruler (or mark the spots with pencil and measure afterwards) to find the distance x from the central maximum to the first-order maximum. Measure to both sides of the central spot (left and right) and take the mean. This cancels any error from the grating not being perfectly centred.
5. Calculate the angle θ
Use trigonometry:
tanθ=Dx
θ=arctan(Dx)
For the small angles typically encountered with first-order maxima and a 1 m screen distance, sinθ≈tanθ≈x/D. However, for higher orders or short screen distances, always use the exact sinθ from the calculated angle.
6. Calculate the wavelength
Rearrange the grating equation:
λ=ndsinθ
For the first-order maximum, n=1, so λ=dsinθ.
7. Repeat for higher orders (if visible)
Measure x for n=2 and n=3 if the spots are clearly visible. Calculate λ from each order. They should all give approximately the same value - if they do, your technique is sound.
Raw Data Table
Your data table should follow the quantity / unit format expected in O-Level practicals. For guidance on table conventions and significant figures, see the Paper 3 marking guide.
Suppose D=1.000 m and the grating has 600 lines/mm (d=1.667×10−6 m):
n
xleft / cm
xright / cm
xmean / cm
θ / degrees
sinθ
λ / nm
1
34.0
34.4
34.2
18.9
0.3239
540
2
76.0
76.6
76.3
37.3
0.6061
505
In practice, the two values of λ should agree closely. Any large discrepancy suggests a measurement error - recheck your distances.
Graph Skills - Multiple Orders
If you measure several orders, a graph provides a cleaner result than averaging individual calculations. For a thorough guide to plotting technique, refer to the graph skills guide.
Plot sinθ on the y-axis against order number n on the x-axis. From the grating equation:
sinθ=dλ⋅n
This is in the form y=mx, a straight line through the origin with gradient:
gradient=dλ
So:
λ=gradient×d
Draw the best-fit line, calculate the gradient using two well-separated points on the line (not data points), and multiply by d to find the wavelength.
Worked Example
Given: A diffraction grating with 600 lines/mm. The screen is placed 100 cm from the grating. The mean distance from the central maximum to the first-order maximum is x=34.2 cm.
Step 1 - Find d:
d=6000001=1.667×10−6m
Step 2 - Find θ:
Convert to metres: x=0.342 m, D=1.000 m.
tanθ=1.0000.342=0.342
θ=arctan(0.342)=18.88°
Step 3 - Find sinθ:
sin(18.88°)=0.3237
Step 4 - Find λ:
For n=1:
λ=dsinθ=1.667×10−6×0.3237=5.40×10−7m=540nm
This is in the green region of the visible spectrum, consistent with a green laser pointer. If you used a red laser (nominal 650 nm), you would expect x to be larger because a longer wavelength diffracts to a wider angle.
The CD Experiment
A compact disc (CD) acts as a reflection diffraction grating. The data is stored in a spiral track with a spacing of approximately 1.6 micrometres between adjacent tracks - close to the slit spacing of a typical 600 lines/mm grating.
What you see
Hold a CD under a desk lamp or sunlight and tilt it. You will see rainbow-coloured bands spreading outward from the reflected light. Each colour appears at a different angle because each wavelength satisfies dsinθ=nλ at a different θ.
Estimating track spacing
You can run the same experiment in reverse. Shine a laser pointer onto the shiny side of a CD at near-normal incidence, and measure the angle to the first-order reflected spot. Since you know the laser wavelength (for example, 650 nm for a red pointer), rearrange to find d:
d=sinθnλ
Typical results give d≈1.5 to 1.7μm, which matches the published track pitch of a CD. A DVD has a tighter track pitch (about 0.74 micrometres), and a Blu-ray disc is tighter still (0.32 micrometres) - which is why they store more data.
This makes a good extension activity and a memorable demonstration of diffraction at work in everyday technology. For a related wave-optics experiment, see the DIY Young's Double-Slit setup.
Sources of Error
Grating not perpendicular to the laser beam
If the grating is tilted, the diffraction spots shift asymmetrically and the measured angles are inaccurate.
Improvement: Check that the central maximum (n=0) hits the screen at the same height as the laser beam exit point. If the grating is perpendicular, the spots on the left and right should be equally spaced from the centre.
Measuring x inaccurately
The diffraction spots have a finite width, and it can be hard to judge the exact centre of a spot, especially for higher orders that are dimmer and broader.
Improvement: Mark the centre of each spot on the screen with a pencil. Measure x to both sides of the central maximum and take the mean to cancel systematic offset. Use a sharp pencil to mark the brightest point of each spot.
Laser not truly monochromatic
Cheap laser pointers may emit a slightly broader band of wavelengths, causing the diffraction spots to appear slightly smeared rather than perfectly sharp.
Improvement: Use a higher-quality laser source. Alternatively, accept a small uncertainty and note it in your evaluation.
Higher orders are faint and hard to locate
Second- and third-order maxima are progressively dimmer because less light is diffracted at steeper angles. In a well-lit room, they may be nearly invisible.
Improvement: Darken the room as much as possible. Use a screen close enough that higher-order spots are bright, but far enough that they are well-separated from each other.
Parallax when measuring distances
If the ruler is not pressed flat against the screen, or your eye is not directly above the marking, you will read the wrong position.
Improvement: Tape the ruler flat to the screen surface. Read markings with your line of sight perpendicular to the ruler.
Common Exam Mistakes
Confusing d (slit spacing) with N (lines per mm). The equation uses d, the distance between adjacent slits, not N, the number of lines per mm. They are reciprocals: d=1/N. If the question states "600 lines per mm," you must convert to d=1.667×10−6 m before substituting into the equation.
Forgetting to convert units. Distances measured in centimetres must be converted to metres before substituting into dsinθ=nλ. Likewise, if N is given in lines per mm, convert to lines per metre first (multiply by 1000), then take the reciprocal to get d in metres.
Using degrees instead of radians in the calculator. When you calculate sinθ or arctan(x/D), make sure your calculator is in degree mode (since we measure θ in degrees here). A common mistake is to leave the calculator in radian mode, which gives a completely wrong angle.
Measuring from the wrong maximum. The central maximum (n=0) is the bright spot straight ahead. The first-order maximum is the next bright spot out to one side. Occasionally students count the central spot as the "first" and measure to what is actually the second order, doubling their error.
Not averaging left and right measurements. If you only measure x to one side, any slight misalignment of the grating will bias your result. Always measure to both sides and take the mean.
Frequently Asked Questions
Why does a diffraction grating give sharper maxima than a double slit? A double slit (two sources) produces broad, smoothly varying fringes. A grating has hundreds or thousands of slits, so the constructive peaks are much narrower and brighter - the more slits, the sharper the maxima. This makes measurements more precise.
Can I use white light instead of a laser? Yes, but the pattern will be different. White light contains all visible wavelengths, so each order (except n=0) spreads into a spectrum - violet closest to the centre, red furthest out. The central maximum remains white because all wavelengths overlap there. This is harder to measure but useful for demonstrating that white light is a mixture of colours.
What happens if I increase the number of lines per mm? A higher line density means a smaller slit spacing d. From dsinθ=nλ, if d decreases, sinθ must increase for the same n and λ. The orders spread further apart, which makes them easier to measure - but fewer orders will be visible before sinθ exceeds 1 (beyond which no maximum exists).
Is the diffraction grating experiment in the O-Level Physics syllabus? The SEAB O-Level Physics 6091 syllabus (for exams from 2026) includes waves and light topics. The diffraction grating equation dsinθ=nλ and the concept of using a grating to measure wavelength are examinable. The experiment is also a strong candidate for Paper 3 planning questions, where you may be asked to design an investigation to determine the wavelength of light.
How accurate is the CD experiment? Using a known laser wavelength and careful angle measurement, you can typically determine the CD track spacing to within 5-10 percent of the published value (1.6 micrometres). It is less accurate than using a proper grating because the CD surface is curved, the track is a spiral rather than straight parallel lines, and the reflection geometry is harder to control. But as a demonstration, it is effective and memorable.
What is the maximum number of orders I can observe? The highest visible order is limited by the condition sinθ≤1. Setting sinθ=1 in the grating equation gives nmax=d/λ. For a 600 lines/mm grating and red light (650 nm): nmax=1.667×10−6/6.50×10−7≈2.6, so you can observe up to the second order. For green light (540 nm), nmax≈3.1, so three orders are possible.
