Physics · Waves & the Particle Nature of Light · AS Level

Interference & Young's Double-Slit Experiment

Shine light through two narrow slits and a screen behind them lights up with evenly spaced bright and dark fringes — one of the most direct pieces of evidence for the wave nature of light. This lesson covers why the pattern appears and how to predict its spacing.

11 min read

Path difference and coherence

Two waves arriving at the same point have usually travelled different distances to get there. The path difference between them is the difference in the lengths of the two paths, measured in metres or (more often) expressed as a number of wavelengths, since it's the path difference relative to $\lambda$ that matters for interference.

Path difference and phase difference describe the same underlying gap between two waves, just in different units. A path difference of one whole wavelength, $\lambda$, corresponds to a phase difference of one whole cycle — $360°$ or $2\pi$ radians — since the waves are back in step. In general, a path difference of $\Delta x$ corresponds to a phase difference of $\dfrac{\Delta x}{\lambda}\times360°$ (or $\dfrac{\Delta x}{\lambda}\times2\pi$ rad). A path difference of $n\lambda$ therefore always gives a phase difference of $n\times360°$ (the waves are in phase), while a path difference of $(n+\tfrac12)\lambda$ gives a phase difference of $(2n{+}1)\times180°$ (the waves are in antiphase).

Coherence means two waves have the same frequency and a constant phase difference — not necessarily zero, just one that doesn't drift randomly over time. This matters because interference relies on a fixed, reproducible relationship between two waves at every point in space; if the phase difference kept changing randomly, the interference pattern would wash out into a uniform average almost instantly.

Two independent, ordinary light sources are never coherent with each other — each emits light in short, random bursts with no fixed phase relationship between them, which is why two separate light bulbs never produce a visible interference pattern. A laser solves this: it produces light very close to a single frequency (monochromatic) and highly coherent along its beam, making it ideal for demonstrating interference and diffraction.

Young's double-slit experiment

Thomas Young's experiment produces two coherent sources from a single source of light, sidestepping the problem of finding two naturally coherent sources. Monochromatic light (from a laser, or a single source passed through a narrow slit first) is directed at a barrier with two narrow, closely spaced parallel slits. Because both slits are illuminated by the same wavefront, light leaving them stays in phase (or at a constant phase difference) — each slit acts as a coherent secondary source derived from the same original wave.

Beyond the slits, light from each spreads out by diffraction and overlaps. Where a screen catches that overlapping light, an interference pattern appears: bright fringes (constructive interference) separated by dark fringes (destructive interference), evenly spaced along the screen.

Animation showing a plane wave travelling rightward and passing through a single narrow slit, diffracting into circular wavefronts. These circular wavefronts travel on and reach a second barrier with two narrow slits, S1 and S2, each of which diffracts the wave into its own expanding circular wavefronts. The two sets of circular wavefronts overlap and cross, producing a criss-cross interference pattern, and as the wavefronts reach a screen on the right, alternating bright and dark vertical fringe bands build up on it, matching the constructive and destructive interference of the overlapping waves. — A single wave diffracts through one slit, then that diffracted wave diffracts again through two slits, producing two coherent circular wave sources whose overlap builds the fringe pattern on the screen.

The pattern arises directly from path difference. At a point equally distant from both slits, light from both arrives in phase — a bright fringe sits directly opposite the midpoint of the two slits. Moving away from that central point, the path difference grows steadily, and with it the phase difference between the two waves arriving there. Wherever the path difference equals a whole number of wavelengths ($0, \lambda, 2\lambda, \dots$), the phase difference is a whole number of cycles ($0°, 360°, 720°, \dots$), so the waves arrive in phase again, giving another bright fringe. Wherever the path difference equals a whole number plus a half ($\tfrac12\lambda, \tfrac32\lambda,\dots$), the phase difference is an odd number of half-cycles ($180°, 540°,\dots$), so the waves arrive in antiphase and cancel, giving a dark fringe.

Deriving the fringe-spacing equation

For slits close together compared with their distance to the screen, the spacing between adjacent bright fringes depends on just three quantities.

Derivationw = λD/s

Let $s$ be the separation of the two slits, $D$ the distance from the slits to the screen, and $\lambda$ the wavelength of the light used. Bright fringes occur wherever the path difference between the two slits equals a whole number of wavelengths, $n\lambda$ — equivalently, wherever the phase difference between the two waves is a whole number of cycles, $n\times360°$.

Since $D$ is always vastly larger than $s$ in this experiment, the two paths from the slits to any given point on the screen are very nearly parallel, so the path difference between them can be treated as $s\sin\theta$, where $\theta$ is the angle between the central axis and the direction to that point.

This is the same small-triangle geometry used later for the diffraction grating — the extra distance one slit's light has to travel is the projection of the slit separation onto the direction of travel.

Because the angles involved are small (again, since $D \gg s$), $\sin\theta \approx \tan\theta \approx \theta$ (in radians), and $\tan\theta = \dfrac{y}{D}$, where $y$ is the distance from the central fringe to the fringe in question, measured along the screen.

Combining these approximations, the path difference becomes $s\sin\theta \approx s\dfrac{y}{D}$.

Setting this equal to $n\lambda$ for the $n$-th bright fringe: $s\dfrac{y_n}{D} = n\lambda$, so $y_n = \dfrac{n\lambda D}{s}$.

The spacing between adjacent fringes, $w$, is the distance between the $n$-th and $(n{+}1)$-th bright fringe: $w = y_{n+1}-y_n = \dfrac{(n{+}1)\lambda D}{s} - \dfrac{n\lambda D}{s} = \dfrac{\lambda D}{s}$.

Every consecutive pair of fringes is separated by the same amount, since the $n$ cancels out — the fringes are evenly spaced.

▪ derived

Here $w$ is the fringe spacing (the distance between adjacent bright, or adjacent dark, fringes), $\lambda$ is the wavelength of the light, $D$ is the distance from the slits to the screen, and $s$ is the separation between the two slits. Because $D$ can be measured accurately and easily made large, and $w$ can be measured directly off the screen, this equation is routinely rearranged to $\lambda = ws/D$ to find the wavelength of light from measurements of the fringe pattern — one of the most direct ways of measuring the wavelength of visible light.

Worked exampleFinding fringe spacing

Laser light of wavelength $\lambda = 590\ \text{nm}$ passes through two slits separated by $s = 0.40\ \text{mm}$, producing an interference pattern on a screen $D = 1.8\ \text{m}$ away. Find the fringe spacing.

Convert to consistent SI units: $\lambda = 590\times10^{-9}\ \text{m}$, $s = 0.40\times10^{-3}\ \text{m}$, $D = 1.8\ \text{m}$.

Substitute into $w = \dfrac{\lambda D}{s}$: $w = \dfrac{(590\times10^{-9})\times1.8}{0.40\times10^{-3}}$.

$w = \dfrac{1.062\times10^{-6}}{4.0\times10^{-4}} \approx 2.66\times10^{-3}\ \text{m} = 2.66\ \text{mm}$.

A fringe spacing of a few millimetres is easily visible and measurable on a screen a couple of metres away — a sensible real-world scale.

▪ answer

Worked exampleFinding wavelength from measured fringe data

In a Required Practical 2 setup, slits separated by $s = 0.50\ \text{mm}$ are placed $D = 2.4\ \text{m}$ from a screen. Ten fringe spacings are measured to span $24.0\ \text{mm}$ across the screen. Find the wavelength of the light used.

Measuring across many fringes rather than just one, then dividing, reduces the percentage error in locating each individual fringe edge: $w = \dfrac{24.0\ \text{mm}}{10} = 2.40\ \text{mm} = 2.40\times10^{-3}\ \text{m}$.

This is standard practical technique — a single fringe spacing is too small to measure precisely, but ten spacings together give a much more reliable average.

Rearrange $w = \dfrac{\lambda D}{s}$ for wavelength: $\lambda = \dfrac{ws}{D}$.

$\lambda = \dfrac{(2.40\times10^{-3})\times(0.50\times10^{-3})}{2.4} = \dfrac{1.2\times10^{-6}}{2.4} = 5.0\times10^{-7}\ \text{m} = 500\ \text{nm}$.

500 nm sits in the middle of the visible spectrum (blue-green light) — a physically sensible answer.

▪ answer

Using white light instead

Repeating the experiment with white light still produces an interference pattern, but the fringes look different. Every wavelength in white light produces its own fringe pattern, and since $w=\lambda D/s$, each gives a different spacing. All wavelengths coincide at the central fringe (zero path difference works for every wavelength), so it stays sharp and white. Moving outward, the fringes for different colours drift out of step and overlap, blurring into smears of colour rather than crisp bands.

Required Practical: Interference Effects (Young's Double Slit and Diffraction Grating)

AQA Required Practical

This is AQA's Required Practical 2: measuring the wavelength of light using double-slit interference and/or a diffraction grating.

Equipment

Equipment	Purpose
Laser (low-power, class 2)	Coherent, monochromatic light source needed for a stable interference/diffraction pattern
Double slit (known slit separation $s$)	Splits the beam into two coherent secondary sources
Diffraction grating (known lines per mm)	Produces sharply defined maxima at angles set by $d\sin\theta=n\lambda$
Screen	Displays the fringe or diffraction pattern for measurement
Metre ruler / tape measure	Measures the slit-to-screen or grating-to-screen distance $D$
Vernier calipers or travelling microscope	Measures fringe spacing precisely, across several fringes at once
Retort stands and clamps	Hold the laser, slit/grating and screen rigidly in line
Laser safety goggles	Eye protection appropriate to the laser class in use

Method

MethodYoung's double slit

Set up the laser so its beam passes through the double slit and falls on a screen a measured distance $D$ away, with the whole arrangement clamped rigidly in a straight line.

Dim the room lighting so the fringe pattern is clearly visible, and measure $D$ from the slits to the screen with a tape measure.

Rather than measuring one fringe spacing, measure the distance spanned by several fringes (e.g. across 10 bright fringes) with vernier calipers or a travelling microscope, then divide by 10 to get the fringe spacing $w$.

Calculate the wavelength using $\lambda = \dfrac{ws}{D}$, using the manufacturer's stated slit separation $s$ (or a value measured separately, e.g. under a microscope).

Repeat at a different value of $D$, or repeat the fringe-spacing measurement several times, and average the resulting wavelengths.

▪ method

MethodDiffraction grating

Direct the laser through the diffraction grating (spacing $d=1/N$, where $N$ is the number of lines per metre) onto a screen or wall a measured distance away.

Identify the diffracted maxima either side of the central spot, and measure the angle $\theta$ to each order — either directly with a spectrometer table, or by measuring the sideways displacement $x$ of each maximum on the screen and the perpendicular distance $D$ to the grating, then calculating $\theta=\arctan(x/D)$.

Use $d\sin\theta=n\lambda$ for each order $n$ measured, and calculate $\lambda$ from each.

Average the wavelengths found from the different orders for a more reliable result.

▪ method

Sources of error and how to minimise them

Measuring across several fringes, not one

A single fringe spacing is small and hard to measure precisely by eye, so a small absolute error in reading it becomes a large percentage error. Measuring across several fringes and dividing by the number of gaps spreads the same absolute reading error over a much larger distance, reducing the percentage uncertainty.

Uncertainty in the slit/grating-to-screen distance $D$

Measure $D$ directly with a tape measure from the plane of the slits/grating to the screen, keeping the whole setup rigidly clamped so nothing shifts between setting up and measuring the pattern.

Ambient light washing out faint fringes

Bright room lighting makes low-intensity outer fringes hard to see and measure accurately. Dim the room, or shield the screen, to improve contrast.

Laser safety

Because lasers are used directly as a coherent light source in this practical, never look directly into the beam or its reflections, keep the beam below eye level at all times, use the lowest laser class that will do the job, and warn anyone else in the room before switching it on.

Key takeaways

Path difference is the difference in distance travelled by two waves reaching the same point; a path difference of $\Delta x$ corresponds to a phase difference of $(\Delta x/\lambda)\times360°$. Coherence means constant frequency and constant phase difference.
A laser provides a monochromatic, coherent source ideal for demonstrating interference and diffraction.
Young's double-slit experiment uses a single wavefront split by two slits to create two coherent secondary sources, producing an interference pattern on a screen.
Bright fringes occur where the path difference is a whole number of wavelengths ($n\lambda$, i.e. a phase difference of $n\times360°$); dark fringes occur where it's a whole number plus a half ($(n+\tfrac12)\lambda$, i.e. a phase difference of an odd multiple of $180°$).
Fringe spacing follows $w = \lambda D/s$, derived from small-angle path-difference geometry — rearranged, this gives a direct way to measure the wavelength of light.
With white light, the central fringe stays white and sharp, but outer fringes blur into colour because each wavelength has a different fringe spacing.
Required Practical 2 investigates interference using Young's slits and a diffraction grating; laser safety (never view the beam directly) applies throughout.

← Previous

Superposition & Standing Waves

Diffraction & the Diffraction Grating