IB Physics SLTopic C.3 — How Waves BehavePaper 1 & 2s = λD/d~8 min read
Young’s Double-Slit Experiment
This is the experiment that proved light is a wave. Shine coherent light through two narrow slits and, instead of two bright patches, you get a whole row of evenly spaced bright and dark fringes — pure interference, made visible, and neatly captured by one equation.
📘 What you need to know
Light passes through a single slit, then a double slit, landing on a screen as a pattern of bright and dark fringes
The light must be coherent (constant phase difference, same frequency) and monochromatic (single wavelength) — hence a laser
Bright fringes (maxima) come from constructive interference; dark fringes (minima) from destructive
The order n labels the fringes: n = 0 is the central maximum, n = 1 the first on each side, and so on
The fringe spacing is given by the double-slit equations = λD/d
Fringes spread out (bigger s) with longer wavelength, a bigger screen distance, or closer slits
The Setup
A laser shines on a single slit, which diffracts the light so it arrives at the double slit as a single coherent wave. The two slits then act as two coherent sources, each diffracting and overlapping with the other. Where the overlapping waves interfere constructively you see a bright fringe; where they interfere destructively you see a dark fringe.
A laser → single slit → double slit (A and B). The two slits behave as coherent sources whose overlapping waves form bright and dark fringes on the screen.
The Interference Pattern
The pattern is a run of equally spaced fringes. Each bright fringe is a maximum of intensity formed by constructive interference (path difference = nλ); each dark fringe is a minimum of zero intensity formed by destructive interference (path difference = (n + ½)λ). The central maximum (n = 0) sits straight ahead where both waves travel equal distances, and every bright fringe has the same width and brightness.
The Double-Slit Equation
The spacing between neighbouring fringes on the screen is given by:
Double-slit fringe spacings = λD / d
The fringe spacing s depends on the wavelength λ, the slit-to-screen distance D and the slit separation d through s = λD/d.
Reading the equation tells you how to spread the fringes further apart: use a longer wavelength, move the screen further away (bigger D), or bring the slits closer together (smaller d).
🧭 Using the double-slit equation
Get the wavelength — from c = fλ if you’re given a frequency
Put everything in metres: mm, nm and cm all convert first
Match the letters: s = fringe spacing, d = slit separation, D = slit-to-screen distance
Substitute into s = λD/d, or rearrange for whichever quantity you need
For a specific bright fringe, use maxima at path difference = nλ
Quick recap: coherent, monochromatic light through a double slit gives evenly spaced fringes — bright = constructive, dark = destructive — with spacing s = λD/d.
WE 1
Two coherent sound sources S₁ and S₂ are 65 cm apart. A microphone sits 150 cm from S₁ along the line at right angles to S₁S₂. The wavelength is slowly increased from 3.5 cm to 12.5 cm.
Determine which orders of maxima are detected at the microphone.
Step 1 — path difference
By Pythagoras the distance from S₂ is √(65² + 150²) = 163 cm
path difference = 163 − 150 = 13 cmStep 2 — maxima at path difference = nλ
So λ = 13/n cm:
n = 1 → 13 cm • n = 2 → 6.5 cm • n = 3 → 4.3 cm • n = 4 → 3.3 cmStep 3 — keep those inside 3.5–12.5 cmOrders n = 2 and n = 3 are detectedn = 1 (13 cm) is too big and n = 4 (3.3 cm) is too small for the wavelength range.
WE 2
A red laser of wavelength 650 nm shines on a double slit with the slits 0.20 mm apart. The screen is 2.0 m away.
Calculate the spacing between adjacent bright fringes.
Convert units
λ = 650 nm = 6.5 × 10⁻⁷ m, d = 0.20 mm = 2.0 × 10⁻⁴ m, D = 2.0 m
Apply s = λD/ds = (6.5 × 10⁻⁷ × 2.0) ÷ (2.0 × 10⁻⁴)s = 6.5 × 10⁻³ m = 6.5 mmTo fit more fringes on the screen you’d close the slits, lengthen the room, or use a redder (longer-wavelength) laser.
💡 Top tips
The light must be coherent and monochromatic — that’s why a laser is used
Bright = constructive (nλ), dark = destructive ((n + ½)λ)
Put s, d and D all in metres before using the equation
Convert a frequency to wavelength first with c = fλ
Bigger s: longer λ, larger D, or smaller d
⚠ Common mistakes
Mixing up d (slit separation) and D (slit-to-screen distance) in the equation
Leaving nm, mm or cm unconverted before substituting
Forgetting the light must be coherent and monochromatic for clear fringes
Swapping the maxima and minima conditions
Reading the fringe spacing as the distance across several fringes rather than one gap
That completes How Waves Behave. You can now handle wavefronts, reflection, refraction, diffraction, superposition and interference — right up to Young’s fringes. The next theme builds on interference with Standing Waves & Resonance.
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