4.9.5Electrons, Waves and Photons
Young’s Double-Slit Experiment
5 min read 5 parts Lesson 58 of 62 Unit quiz
Section 1 of 5Setting Up the Experiment
Single slit
- Light from a monochromatic source passes through one narrow slit first, so the light reaching the double slit comes from a single source.
Double slit
- The light diffracts at each of the two slits, which then behave as two coherent sources that are in phase.
Screen
- Overlapping diffracted waves meet on a distant screen where they form a pattern of alternating bright and dark fringes.
Monochromatic
- Using one wavelength keeps the fringes sharp, because white light would spread the maxima into overlapping colours.
Section 2 of 5Why Fringes Form
Why Fringes Form
Bright fringe
- Waves from the two slits arrive in phase because the path difference is nλ, giving constructive interference.
Dark fringe
- Waves arrive in antiphase when the path difference is (n + ½)λ, giving destructive interference.
Order n
- The central bright fringe is order zero, and the orders count outwards on both sides of it.
Wave evidence
- Particles could not cancel each other, so an interference pattern supports the wave model of light.
Section 3 of 5The Double-Slit Equation
Equation
- λ = ax ÷ D, where a is the slit separation, x the fringe separation and D the slit-to-screen distance.
Fringe separation
- Rearranging gives x = λD ÷ a, so x is directly proportional to wavelength and to D.
Slit separation
- Closer slits (smaller a) produce wider fringes, which makes the pattern easier to measure.
Condition
- The equation is valid when a is much smaller than D, so that the angles involved are very small.
Colour
- Red light has a longer wavelength than blue, so red fringes are spaced further apart.
| Change | Effect on fringe separation x |
|---|---|
| Increase D | Increases |
| Decrease a | Increases |
| Use a shorter wavelength | Decreases |
Section 4 of 5Worked Example
Question
- Light of wavelength 633 nm illuminates two slits 0.25 mm apart.
- The screen is 2.0 m from the slits.
- Calculate the fringe separation.
- Convert unitsλ = 633 × 10⁻⁹ m and a = 0.25 × 10⁻³ m.
- Rearrangex = λD ÷ a.What the symbols mean: λ = wavelength (m) · a or s = slit separation (m) · x or w = fringe spacing (m) · D = slit-to-screen distance (m)
- x = (633 × 10⁻⁹ × 2.0) ÷ (0.25 × 10⁻³) = 5.06 × 10⁻³ m.
Answer x ≈ 5.1 mm (5.06 mm before rounding).
Section 5 of 5Exam Checklist & Tips
4.9.5 – Key Points for the Exam
- Monochromatic Light of a single wavelength or very narrow range of wavelengths.
- Fringe separation The distance between the centres of adjacent bright (or dark) fringes, symbol x.
- Coherent Having a constant phase difference between the two sources.
- Diffraction The spreading of a wave as it passes through a gap comparable with its wavelength.
Common Mistakes
- Mixing up a and x; remember a is the slit gap, x is the fringe gap, D is to the screen.
- Forgetting to convert millimetres and nanometres into metres.
- Measuring from the middle of one fringe to the edge of another instead of centre to centre.
- Claiming the pattern is caused by two bulbs; the slits must be fed by one source.