Use Young’s double-slit equation
Relate fringe spacing to wavelength, slit separation and screen distance using λ = ax/D.
AS Level; Cambridge International Physics 9702, 2025–2027 syllabus, Topic 8. These original models and calculations are study aids; full timed assessment, supervised practical competence and human subject-teacher review remain outstanding.
Before you begin
- Use wavelength, frequency, phase difference, trigonometry and consistent SI units.
Work on paper. Try each question before revealing help, and explain why your method works.
Quick readiness check
In λ = ax/D, what does x represent?
What you will learn
- Recall and use λ = ax/D for double-slit interference
- Identify fringe spacing, slit separation and screen distance
- Rearrange and apply the equation with compatible units
Double-slit geometry sets the fringe spacing
For two narrow slits separated by distance a and a screen distance D away, the small-angle double-slit model gives x = λD/a, where x is the spacing between adjacent bright fringes. Rearranging gives λ = ax/D.
Use all distances in the same units before calculating. Increasing wavelength or screen distance increases fringe spacing; increasing slit separation decreases it. The equation applies to the stated double-slit interference arrangement, not to a diffraction grating.
Measure adjacent-fringe spacing carefully
Measure the distance spanning several adjacent fringe intervals and divide by the number of intervals to estimate x. Measuring multiple intervals reduces the effect of a single ruler reading uncertainty.
Use D from the slit plane to the screen, and a as the separation of the two slits. Keep x distinct from the distance from the central maximum to one fringe: that distance may span several x intervals.
Pause and explain
If D doubles with λ and a fixed, what happens to x?
Worked example
Slits 0.25 mm apart produce adjacent bright fringes 2.4 mm apart on a screen 1.5 m away. Find wavelength.
Show the worked solution
- Convert a = 0.25 mm = 2.5 × 10⁻⁴ m and x = 2.4 mm = 2.4 × 10⁻³ m.
- λ = ax/D = (2.5 × 10⁻⁴)(2.4 × 10⁻³)/1.5.
- Evaluate in metres.
Answer λ = 4.0 × 10⁻⁷ m = 400 nm.
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Write your answer and reasoning first. Use a hint only if you are stuck. The model solution is for self-checking; your written work is not automatically marked.
A = 0.30 mm, D = 2.0 m and adjacent-fringe spacing x = 3.0 mm. Calculate wavelength.
Give me a hint
Convert both millimetre quantities to metres and use λ = ax/D.
Compare my reasoning
- a = 3.0 × 10⁻⁴ m and x = 3.0 × 10⁻³ m.
- λ = (3.0 × 10⁻⁴)(3.0 × 10⁻³)/2.0.
- Evaluate and state the result in metres.
λ = 4.5 × 10⁻⁷ m.
Look for these in your work
- Units converted
- Correct equation used
- Wavelength unit stated
Light of wavelength 5.0 × 10⁻⁷ m passes through slits separated by 0.20 mm. The screen is 2.0 m away. Find fringe spacing.
Give me a hint
Rearrange to x = λD/a and convert slit separation to metres.
Compare my reasoning
- a = 0.20 mm = 2.0 × 10⁻⁴ m.
- x = (5.0 × 10⁻⁷ × 2.0)/(2.0 × 10⁻⁴).
- Give spacing in metres or millimetres.
x = 5.0 × 10⁻³ m = 5.0 mm.
Look for these in your work
- Equation rearranged
- Slit separation converted
- Fringe spacing calculated
A screen shows bright fringes at 12.0 mm and 20.4 mm from the central maximum, with no bright fringe between them. Find adjacent spacing x and explain why their separation is not 8.4 mm for one interval.
Give me a hint
Count the number of adjacent intervals between the measured bright fringes.
Compare my reasoning
- There is one intermediate bright fringe, so the two measured positions are two intervals apart.
- Total separation = 20.4 − 12.0 = 8.4 mm.
- x = 8.4/2 = 4.2 mm.
Adjacent fringe spacing is 4.2 mm; the 8.4 mm distance spans two equal intervals.
Look for these in your work
- Intervals counted
- Position difference calculated
- Per-interval spacing obtained
Common mistakes
- Using the distance to the screen as the slit separation
- Using central-to-fringe distance when the question gives several fringe intervals
- Mixing millimetres and metres in one substitution
What can you explain now?
In λ = ax/D, what does x represent?
Compare with the explanation
Spacing between adjacent fringes
x is the fringe separation in the double-slit pattern.
After trying it yourself, choose your next review. This is your self-assessment.
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Make it stick
How can measuring several fringe intervals improve an estimate of wavelength?
If you needed the solution, close it and solve the problem again from a blank page. A correct answer is stronger when you can explain the reason for each step.