Two-source interference and Young double slit
Key idea: H2 Physics lessons on progressive-wave models, standing waves, interference, diffraction and resolution.
Continue where you stopped
The core idea
Build the idea
Learn the idea
Big question: How does path difference decide whether waves reinforce or cancel?
Coherent sources maintain a constant phase difference. For in-phase sources, maxima occur where path difference is nλ and minima where it is (n + 1/2)λ. In Young's double-slit experiment, coherent illumination and small angles give fringe spacing x = λD/a.
Distinguish superposition from stable interference
Superposition means resultant displacement is the algebraic sum of overlapping displacements. A stable interference pattern requires coherent sources: the same frequency and a constant phase difference. Two independent lamps do not maintain that relationship.
The same idea appears as large and small ripple-tank amplitudes, loud and quiet regions from coherent sound sources, detector maxima and minima for microwaves, and bright and dark light fringes. For two in-phase sources, constructive interference occurs at path difference nλ and destructive interference at (n + ½)λ.
Check your understanding: What is the phase difference for path difference 3λ/4?
2π(3/4) = 3π/2 rad, equivalent to −π/2 rad.
Understand Young's double-slit geometry
One slit illuminates two narrow slits so they act as coherent sources. Far from slits separated by a, the path difference at angle θ is a sinθ. For small angles, y ≈ Dθ, giving fringe spacing w = λD/a.
The small-angle result needs D much larger than slit separation and y small relative to D. Increasing wavelength or screen distance increases fringe spacing; increasing slit separation decreases it. Fringe position and fringe visibility are different ideas.
Check your understanding: Which change doubles fringe spacing without changing wavelength?
Double screen distance D or halve slit separation a, within the small-angle model.
Key ideas to keep
- A stable pattern needs coherence, not merely equal frequencies at one instant.
- Path difference and phase difference are related but have different units.
- Increasing slit separation decreases fringe spacing.
See the reasoning
Worked example
Find wavelength from fringe data
Question: Slits 0.30 mm apart produce fringes 4.0 mm apart on a screen 2.0 m away. Find the wavelength.
Step 1: Convert all lengths to metres
Why: The fringe formula is dimensionally consistent only with one unit system.
Working: a = 3.0×10⁻⁴ m, w = 4.0×10⁻³ m, D = 2.0 m.
Step 2: Rearrange the small-angle equation
Why: Fringe spacing, rather than one fringe position, is supplied.
Working: λ = wa/D.
Step 3: Substitute and check scale
Why: Visible wavelengths are hundreds of nanometres.
Working: λ = (4.0×10⁻³)(3.0×10⁻⁴)/2.0 = 6.0×10⁻⁷ m.
Answer: The wavelength is 6.0 × 10⁻⁷ m, or 600 nm.
Check: The result lies in the visible range, supporting the unit conversion.
Another worked model
Question
Two coherent water waves of wavelength 0.120 m reach a point with path difference 0.300 m. Find phase difference and classify the interference.
Check the worked solution
Path difference is 0.300/0.120 = 2.5 wavelengths, so Δφ = 2π(2.5) = 5π rad, equivalent to π rad. The waves arrive in antiphase and interfere destructively if their amplitudes are equal.
Use a hint if needed
Practise with support
Try this
Two coherent sources have wavelength 0.50 m. At P their path difference is 1.25 m. Find phase difference and classify P.
Hint: Convert path difference to wavelengths before deciding integer or half-integer.
Check your answer
1.25/0.50 = 2.5 wavelengths, so Δφ = 5π rad, equivalent to π. P is a destructive minimum for equal amplitudes.
Now work without the hint
Practise independently
Your turn
Derive x = λD/a for adjacent Young double-slit fringes using small-angle geometry and state two visibility conditions beyond the path-difference rule.
Check your answer
For a point at transverse distance y, path difference ≈ a sinθ ≈ ay/D. Adjacent maxima differ by one λ, so aΔy/D = λ and x = λD/a. Sources must be coherent, and waves must overlap with compatible polarisation and sufficiently similar amplitudes.
Avoid these traps
Common mistakes
Common mistake
Same frequency alone guarantees stable interference fringes.
What is wrong with this reasoning?
Show better thinking
The sources must maintain a constant phase difference, and the waves must overlap with compatible polarisation and useful amplitude contrast.
Write for the examiner
Exam guidance
State the small-angle condition and keep slit separation a distinct from fringe spacing x.
Exam-style practice [8 marks]
Explain how a double-slit pattern is formed and predict the effects on fringe spacing and visibility when one slit is narrowed substantially.
Plan before you answer
- Explain coherence and path difference.
- Use the spacing equation for positions.
- Treat unequal amplitudes separately from spacing.
Mark your answer and compare the model
Marking points
Tick each point only if your answer states it clearly.
Model answer
The two slits are fed by the same wavefront, so they have one frequency and a constant phase relationship. At the screen, path differences nλ give constructive interference and (n+½)λ give destructive interference. The spacing w = λD/a is unchanged because slit separation a is unchanged. Narrowing one slit reduces its amplitude, so cancellation at a nominal minimum is incomplete and fringe visibility decreases.
Come back in three days
Check what stayed with you
Recall question 1
Define coherent sources.
Check the answer
Sources with the same frequency and a constant phase difference.
Recall question 2
State constructive path difference for in-phase sources.
Check the answer
nλ.
Recall question 3
State the Young fringe-spacing equation.
Check the answer
w = λD/a for small angles.
Syllabus and review details
This lesson covers the listed H2 Physics 9478 outcomes. Topic 10 states no explicit exclusions. Topic 11(j) does not require knowledge of spectrometer structure or use. Graph interpretations distinguish time traces at one position from spatial profiles at one instant, and all small-angle equations are used only with their stated geometry.
- GCE A-Level H2 PhysicsTopic 11(e) / Topic 11(f) / Topic 11(g) / Topic 11(h) · 2027Checked against the syllabus · partial topic coverageOfficial 9478 syllabus
Course and syllabus information
- Course
- GCE A-Level H2 Physics
- Edition
- GCE A-Level H2 Physics 2027