Young's Double Slit Experiment

Thomas Young's double slit experiment (1801) provided the first conclusive evidence that light behaves as a wave. It remains one of the most important experiments in physics and is a required part of the AQA A-Level specification.

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Experimental Setup

The apparatus consists of:

1. A single light source (e.g., a sodium lamp or laser)
2. A single slit — to act as a coherent point source (not needed if using a laser)
3. A double slit — two narrow, parallel slits separated by a distance s (typically ~0.1–0.5 mm)
4. A screen placed at a distance D from the double slit (typically 1–2 m)

Light from the single source passes through the double slit. Each slit acts as a separate coherent source (because they originate from the same wavefront). The two sets of diffracted waves overlap and interfere on the screen.

Why a Single Slit First?

When using a non-laser source, a single slit is placed before the double slit to ensure spatial coherence. The single slit produces a single diffraction pattern, illuminating both slits of the double slit with light from the same wavefront. This guarantees a constant phase relationship between the two slits.

A laser already produces spatially coherent light, so the single slit can be omitted.

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The Fringe Pattern

On the screen, an alternating pattern of bright fringes (maxima) and dark fringes (minima) is observed:

• Bright fringes occur where the waves from the two slits arrive in phase (constructive interference).
• Dark fringes occur where the waves arrive in antiphase (destructive interference).

The fringes are equally spaced (for small angles) and parallel to the slits. The central bright fringe (zeroth order, n = 0) is on the axis of symmetry, where the path difference is zero.

Fringe Spacing Equation

The distance between adjacent bright fringes (or adjacent dark fringes) is called the fringe spacing (or fringe width), w:

w = λD/s

where:

• w = fringe spacing (m)
• λ = wavelength of light (m)
• D = distance from the double slit to the screen (m)
• s = separation of the two slits (centre to centre) (m)

Derivation

Consider the nth bright fringe at a position y on the screen, measured from the central maximum. For a bright fringe, the path difference from the two slits must equal nλ.

Using geometry, for small angles θ:

• Path difference = s sin θ ≈ s tan θ = s × (y/D)
• For the nth maximum: s × (y/D) = nλ
• So y = nλD/s

The spacing between the nth and (n+1)th maxima is: w = y(n+1) − y(n) = (n+1)λD/s − nλD/s = λD/s

Exam Tip: This derivation requires the small angle approximation (sin θ ≈ tan θ ≈ θ for small θ in radians). This is valid when D >> s, which is always the case in practice.

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Worked Examples

Worked Example 1 — Red laser light of wavelength 635 nm passes through a double slit with slit separation 0.40 mm. The screen is 2.5 m from the slits. Calculate the fringe spacing.

λ = 635 nm = 635 × 10⁻⁹ m = 6.35 × 10⁻⁷ m s = 0.40 mm = 4.0 × 10⁻⁴ m D = 2.5 m

w = λD/s = (6.35 × 10⁻⁷ × 2.5)/(4.0 × 10⁻⁴)

w = (1.5875 × 10⁻⁶)/(4.0 × 10⁻⁴) = 3.97 × 10⁻³ m

w = 4.0 × 10⁻³ m = 4.0 mm

Worked Example 2 — In a Young's double slit experiment, the fringe spacing is measured as 2.8 mm when the slit-to-screen distance is 1.80 m and the slit separation is 0.35 mm. Calculate the wavelength of the light.

w = 2.8 mm = 2.8 × 10⁻³ m D = 1.80 m s = 0.35 mm = 3.5 × 10⁻⁴ m

Rearranging w = λD/s:

λ = ws/D = (2.8 × 10⁻³ × 3.5 × 10⁻⁴)/1.80

λ = (9.80 × 10⁻⁷)/1.80 = 5.44 × 10⁻⁷ m