Interference & Diffraction of Light

Interference & Diffraction

When two waves meet, some places constructively brighten and others destructively darken into an interference pattern. In Young's double slit, path difference of integer wavelengths builds up light; odd half-wavelengths cancel. Changing slit spacing, wavelength, or slit width changes fringe spacing and diffraction. Slide slit distance, wavelength, and slit width here to watch the interference and diffraction fringes.

What is Interference?

💡 When Two Waves Meet

①Drop two stones in a lake — overlapping ripples appear

②Some places amplify (constructive), some cancel (destructive)

③Light is a wave too — two beams produce bright and dark stripes

④This is the interference pattern — decisive evidence that light is a wave!

Young's Double-Slit Experiment

Slit spacing d3

Wavelength λ5

Constructive Condition

d sin θ = mλ (m = 0, ±1, ±2, …)

Path difference = integer multiples of λ → constructive (bright)

Destructive Condition

d sin θ = (m + 12)λ

Path difference = half-integer multiples → destructive (dark)

📐 Why Path Difference Matters

①Light from two slits reaches a point on the screen

②Difference in travel distance = path difference

③Path diff = mλ → crest+crest = constructive (bright)

④Path diff = (m+½)λ → crest+trough = destructive (dark)

⑤This yields d sin θ = mλ

Fringe Spacing and Variables

Bright Fringe Spacing

Δy = λLd

Distance between adjacent bright fringes on the screen

🔑 Which Variables Change the Pattern?

①d (slit spacing) ↓ → Δy ↑ (wider spacing)

②λ ↑ → Δy ↑

③L ↑ → Δy ↑

④Red light (large λ) has wider spacing than violet (small λ)

Single-Slit Diffraction

Slit width a3

Single-Slit Dark Fringe

a sin θ = mλ (m = ±1, ±2, …)

mth dark fringe for slit width a

Comparison

ChartDouble-Slit vs Single-Slit

Item	Double-Slit Interference	Single-Slit Diffraction
Sources	2 (two slits)	1 (within a single slit)
Bright fringes	Path diff = mλ	Brightest at center
Dark fringes	Path diff = (m+½)λ	a sinθ = mλ
Pattern	Equally spaced stripes	Wide center, narrow sides
Real observation	Interference within diffraction envelope	Diffraction only

🌈 Interference and Diffraction in Daily Life

①Soap bubble colors = thin film interference

②CD/DVD rainbow = diffraction grating

③Oil film rainbow = interference of reflections at two interfaces

④All these confirm the wave nature of light

Worked Examples

Example 1

A double slit with spacing d = 0.2 mm and light of λ = 600 nm shines on a screen L = 2 m away. What is the bright-fringe spacing Δy?

Use the fringe-spacing formula Δy = λL/d.

Δy = λLd

Substitute λ = 6×10⁻⁷ m, L = 2 m, d = 2×10⁻⁴ m.

Δy = 6×10^-7 × 22×10^-4 = 6×10^-3 m = 6 mm

▸ 6 mm

Fringe spacing Δy = λL/d. Smaller slit spacing d, or larger wavelength and screen distance, widens the fringes.

Example 2

With the same double slit, if only the light changes from red (λ = 700 nm) to violet (λ = 400 nm), by what factor does the fringe spacing change?

In Δy = λL/d, with d and L fixed, Δy is proportional to λ.

Δy ∝ λ (d, L fixed)

Apply the wavelength ratio directly.

Δy_violetΔy_red = 400700 = 47

▸ 4/7

Fringe spacing is proportional to wavelength. Violet (smaller λ) gives tighter fringes than red.

Summary

Key Formulas

d sin θ = mλ, Δy = λLd

Double-slit constructive condition + fringe spacing

CSAT-style

In Young’s double-slit experiment, if only the slit spacing d is doubled, how does the bright-fringe spacing Δy change?

①2×

②4×

③12×

④14×

⑤No change

▸ ③ 12×

Fringe spacing Δy = λL/d is inversely proportional to the slit spacing d.

Δy = λLd

If d doubles, Δy is halved.

d→2d ⇒ Δy ∝ 12d = 12Δy

🎯 Exam Points

①Constructive: d sinθ = mλ → bright (integer-multiple path diff)

②Destructive: d sinθ = (m+½)λ → dark

③Spacing: Δy = λL/d (d↓, λ↑, L↑ → wider spacing)

④Single-slit dark: a sinθ = mλ

⑤Interference/diffraction → wave / photoelectric → particle

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