Young's Double-Slit Experiment

In 1801, the English polymath Thomas Young performed an experiment that settled a century-long debate about the nature of light. He passed a single beam of light through two closely-spaced slits and observed, on a screen placed some distance beyond, a pattern of alternating bright and dark fringes. This pattern could only be explained if light were a wave — particles would have produced two isolated bright patches, one behind each slit, but not a fringe pattern. Young's experiment remains the canonical demonstration of wave interference and is one of the most important experiments in the history of physics.

At A-Level, you are expected to describe the experiment, explain the fringe pattern qualitatively, and apply the double-slit formula:

λ = a x / D (equivalently, x = λD/a)

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The Set-Up

A typical modern Young's experiment uses the following apparatus.

1. A monochromatic, coherent light source — most commonly a laser, because it is naturally monochromatic and spatially coherent. Historically, Young used sunlight passed through a narrow primary slit to create a coherent source.
2. Two parallel slits, very narrow, separated by a small distance a (the slit separation, typically 0.1–0.5 mm).
3. A screen placed a distance D beyond the slits (typically 1–3 m).
4. The resulting fringe pattern — alternating bright and dark fringes — observed on the screen. The bright-to-bright spacing is the fringe spacing x.

flowchart LR
    L[Laser: coherent, monochromatic] --> S1[Slit 1]
    L --> S2[Slit 2]
    S1 --> P[Point on screen]
    S2 --> P
    P --> V[Resultant: bright or dark depending on path difference]
    V --> BR[Bright fringes at path difference = n lambda]
    V --> DK[Dark fringes at path difference = n plus half lambda]

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How the Pattern Forms

The two slits act as sources of secondary waves (Huygens's principle). Because both slits are illuminated by the same primary wave, they emit light that is automatically coherent (same frequency, constant phase relationship).

At any point on the screen, waves from the two slits arrive having travelled slightly different distances. The path difference between the two waves determines whether they interfere constructively or destructively at that point:

• Bright fringe (constructive): path difference = n λ, where n = 0, ±1, ±2, …
• Dark fringe (destructive): path difference = (n + ½) λ, where n = 0, ±1, ±2, …

Where they are in phase, crests add to crests and amplitudes double (intensity quadruples) — a bright fringe. Where they are in antiphase, crests cancel troughs and the intensity drops to zero — a dark fringe.

The result is a regular series of equally-spaced bright and dark fringes on the screen, symmetric about the central maximum (directly between the two slits).

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The Double-Slit Formula: Derivation

Let the two slits be separated by a distance a, and the screen be at a distance D from the slits. Consider a point on the screen at a distance y from the central maximum.

For small angles (D >> a and D >> y, which are always satisfied in a laboratory Young's experiment):

path difference Δ ≈ a y / D

The condition for the nth bright fringe is:

a y_n / D = n λ y_n = n λ D / a

Adjacent bright fringes therefore differ in y by:

x = y_{n+1} − y_n = λ D / a

Rearranging for wavelength:

λ = a x / D

This is the formula OCR expects you to know.

Variables in the Formula

Symbol	Meaning	Typical value
λ	Wavelength of the light	400–700 nm for visible
a	Slit separation	0.1–1.0 mm
x	Fringe spacing (bright-to-bright or dark-to-dark)	1–10 mm
D	Slit-to-screen distance	1–3 m

The formula is valid when a << D and y << D, which together guarantee the small-angle approximation sin θ ≈ tan θ ≈ θ. At A-Level this approximation is always assumed.

Exam Tip: OCR sometimes writes the formula as λ = ay/D or λ = aw/D — different textbooks use different letters for fringe spacing. Always state which symbol you mean. The formula is also sometimes quoted as y = nλD/a for the position of the nth bright fringe from the centre.

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Worked Example 1 — Finding the Wavelength

Q. In a Young's double-slit experiment, the slit separation is 0.40 mm and the distance to the screen is 1.50 m. The fringe spacing is measured to be 2.25 mm. Calculate the wavelength of the light.

A. Using λ = ax/D with a = 4.0 × 10⁻⁴ m, x = 2.25 × 10⁻³ m, D = 1.50 m:

λ = (4.0 × 10⁻⁴) × (2.25 × 10⁻³) / 1.50 λ = 6.00 × 10⁻⁷ m = 600 nm

This lies in the orange part of the visible spectrum.

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Worked Example 2 — Predicting Fringe Spacing

Q. Light of wavelength 450 nm illuminates two slits 0.25 mm apart. A screen is placed 1.20 m away. Calculate the fringe spacing.

A.