Module 4 · Electrons, Waves and Photons

Young's Double Slit Experiment

Specification: OCR A H556 | Section: 4.4.3 Superposition | Focus: interference, coherence, path difference and fringe spacing

By the end of this topic you should be able to…

describe the Young double slit setup and the observed fringe pattern
explain why coherent, monochromatic light is required
use path difference to explain constructive and destructive interference
apply the OCR fringe spacing equation x = λD / a correctly and with consistent units
avoid common mistakes about phase, spacing and screen distance

Big idea: the double slit experiment gave powerful classical evidence that light behaves as a wave, because it produces an interference pattern of alternating bright and dark fringes.

Part 1

Setup and observations

In Young’s double slit experiment, monochromatic light from a source first passes through a single slit so that the light reaching the double slit is coherent. The light then passes through two closely spaced slits and falls on a distant screen.

Single slit

Acts as a common source so the two slits are illuminated by waves with a fixed phase relationship.

Double slit

Acts as two coherent sources producing overlapping waves on the screen.

Screen

Shows a series of equally spaced bright and dark fringes.

The pattern observed is:

a bright central fringe
alternating bright and dark fringes on either side
approximately equal fringe spacing when the small-angle approximation is valid

OCR exam point

Young’s double slit experiment is important because it shows interference of light and therefore gives evidence for the wave nature of light.

Part 2

Coherence, path difference and interference

Coherent sources are sources that emit waves of the same frequency with a constant phase difference. Without coherence, the bright and dark fringes would wash out.

Constructive interference

Bright fringes occur where the waves arrive in phase.

Bright fringe conditionpath difference = nλ where n = 0, 1, 2, 3 …

Destructive interference

Dark fringes occur where the waves arrive out of phase by 180°.

Dark fringe conditionpath difference = (n + 1/2)λ

Common misconception

The central fringe is bright, not dark, because the path difference there is zero, which is constructive interference.

Path difference is the difference in the distance travelled by the two waves from the slits to a particular point on the screen.

Part 3

Fringe spacing equation

Using OCR notation, for slit separation a, screen distance D, wavelength λ, and fringe spacing x:

Fringe spacing equationx = λD / a

This comes from the small-angle approximation, so it works when the screen is far from the slits and the fringe positions are close to the centre compared with the screen distance.

Unit discipline

Always convert all quantities to SI units before substituting: λ in metres, D in metres, s in metres, so w comes out in metres.

What changes the fringe spacing?

Increase wavelength λ → fringe spacing increases
Increase screen distance D → fringe spacing increases
Increase slit separation a → fringe spacing decreases

Worked example 1

A laser of wavelength 632 nm passes through a double slit with slit separation 0.30 mm. The screen is 2.4 m away. Calculate the fringe spacing.

Convert units: λ = 6.32 × 10⁻⁷ m, a = 3.0 × 10⁻⁴ m

Use x = λD / a = (6.32 × 10⁻⁷ × 2.4) / (3.0 × 10⁻⁴)

x = 5.1 × 10⁻³ m = 5.1 mm

Worked example 2

The fringe spacing is 2.0 mm when the slit separation is 0.25 mm and the screen distance is 1.5 m. Find the wavelength.

Rearrange: λ = ax / D

Use SI units: x = 2.0 × 10⁻³ m, a = 2.5 × 10⁻⁴ m

λ = (2.0 × 10⁻³ × 2.5 × 10⁻⁴) / 1.5 = 3.3 × 10⁻⁷ m = 330 nm

Interactive

Interference pattern simulator

Fringe spacing x: 3.30 mm

Pattern colour: green

Trend: baseline

Part 4

Required conditions and practical issues

Why monochromatic light?

If the light contains many wavelengths, each wavelength produces a slightly different fringe spacing. The result is coloured fringes near the centre and overlapping blur further out, not a clean pattern.

Why coherent light?

If the phase difference changes randomly, the bright and dark fringes do not remain fixed. That is why a laser or a single slit feeding the double slit is used.

Increase D

Fringes spread out more and become easier to measure, though the pattern may become dimmer.

Decrease s

Fringes spread out because w is inversely proportional to slit separation.

Measure many fringes

Measure across several fringe spacings, then divide by the number of gaps for improved precision.

Common mistakes

Students often confuse slit width with slit separation, mix up mm and m, or think increasing slit separation makes fringes further apart. It actually makes them closer together.

Knowledge

Knowledge Check

Why must the two slits act as coherent sources?

2 marks

They must have the same frequency
They must maintain a constant phase difference so a stable fringe pattern forms

What path difference produces the third bright fringe from the centre?

1 mark

Path difference = 3λ

If the wavelength increases and everything else stays the same, what happens to fringe spacing?

1 mark

Fringe spacing increases

Exam Practice

Exam-Style Questions

Young’s double slit experiment produces a series of bright and dark fringes on a screen.

Explain how this pattern is formed and why it provides evidence for the wave nature of light.

5 marks

Light from the two slits overlaps on the screen
The two slits act as coherent sources
Bright fringes are formed by constructive interference where path difference = nλ
Dark fringes are formed by destructive interference where path difference = (n + 1/2)λ
Interference is a wave phenomenon, so the pattern shows that light behaves as a wave

A student uses a laser of wavelength 635 nm in a Young double slit experiment. The slit separation is 0.24 mm and the screen is 2.8 m from the slits.

(a) Calculate the fringe spacing x. [3 marks]
(b) The student measures the distance across 12 fringes. Calculate this distance. [2 marks]
(c) State one reason why measuring across several fringes is better than measuring one fringe spacing directly. [1 mark]

6 marks

(a) λ = 6.35 × 10⁻⁷ m, a = 2.4 × 10⁻⁴ m
x = λD / a = (6.35 × 10⁻⁷ × 2.8) / (2.4 × 10⁻⁴) = 7.41 × 10⁻³ m
x = 7.41 mm
(b) Distance across 12 fringes = 12x = 88.9 mm
(c) Reduces percentage uncertainty / gives more precise value for x

Describe the conditions needed to obtain a clear interference pattern in Young’s double slit experiment.

4 marks

The two slits must be illuminated by coherent light / constant phase difference
The light should be monochromatic
The slits should be narrow and close together
The screen should be sufficiently far away so fringes are distinct / small-angle approximation is valid

A student says, “The central fringe is dark because the two waves meet there first.” State whether this is correct and explain your answer.

3 marks

The statement is incorrect
At the centre, the path difference is zero
Zero path difference gives constructive interference, so the central fringe is bright

In a Young double slit experiment the slit separation is doubled while the wavelength and screen distance remain constant.

Which statement is correct?
A. The fringe spacing doubles
B. The fringe spacing halves
C. The fringe spacing is unchanged
D. The central fringe disappears

1 mark

B is correct because x = λD / a, so doubling a halves x

The distance across 10 fringe spacings in a Young double slit experiment is measured as 32 mm. The wavelength of the light is 5.8 × 10⁻⁷ m and the screen is 1.6 m from the slits.

Calculate the slit separation a.

4 marks

x = 32 mm / 10 = 3.2 mm = 3.2 × 10⁻³ m
Rearrange x = λD / a to get a = λD / x
a = (5.8 × 10⁻⁷ × 1.6) / (3.2 × 10⁻³)
a = 2.9 × 10⁻⁴ m = 0.29 mm

Topic Summary

Interference

Bright fringes come from constructive interference; dark fringes come from destructive interference.

Coherence

The two slits must act as coherent sources with constant phase difference.

Fringe spacing

w increases with wavelength and screen distance, but decreases with slit separation.

Evidence

Young’s experiment is classic evidence for the wave nature of light.

x = λD / a

bright: nλ

dark: (n + 1/2)λ

coherent + monochromatic