seegongsik
Grade 11-12 (age 16-18)

high school physics Interference & Diffraction of Light

Interference & Diffraction

Where two waves overlap, in some places they build each other up and grow bright, and in others they cancel and go dark, so bright and dark bands alternate. This is interference. In Young's double-slit experiment, the screen is bright where the path difference between light from the two slits is a whole number of wavelengths, and dark where it is an odd number of half wavelengths. The spacing between bright fringes is Δy = λL/d, so it widens with longer wavelength and narrower slit spacing, and light through a single slit also spreads out by diffraction and forms a pattern. In the picture, changing the slit spacing and the wavelength changes the spacing of the bands on the screen, and changing the slit width changes the width of the central bright band.

What is Interference?

💡 When Two Waves Meet
①Throw two stones into a lake at the same moment and the two sets of ripples overlap in places
②In some places crest meets crest and the ripples grow (constructive interference); in others crest meets trough and the water goes calm (destructive interference)
③Light is a wave too, so where two beams overlap, bright and dark bands alternate
④This interference pattern is strong evidence that light is a wave
⑤Interference and diffraction are evidence of the wave nature of light, and the photoelectric effect is evidence of its particle nature

Young's Double-Slit Experiment

3
5
Constructive Condition
d sin θ = mλ (m = 0, ±1, ±2, …)
When the path difference is a whole number of wavelengths, the waves reinforce and a bright fringe appears
Destructive Condition
d sin θ = (m + 12)λ
When the path difference is an odd number of half wavelengths, the waves cancel and a dark fringe appears
📐 The Path Difference Decides the Pattern
①Light leaving the two slits arrives at one point on the screen
②The difference in the distances the two beams travel is the path difference
③When the path difference is mλ, crest meets crest and the point is bright; from m = 0 in the middle, the bright fringes m = 1, 2, … line up above and below
④When the path difference is (m + ½)λ, crest meets trough and the point is dark
⑤When the screen is far away the path difference equals d sin θ, so the condition for a bright fringe is d sin θ = mλ

What Changes the Fringe Spacing

Bright Fringe Spacing
Δy = λLd
The distance between neighboring bright fringes on the screen
🔑 Which Variables Change the Pattern
①Reducing the slit spacing d widens the fringe spacing Δy
②The longer the wavelength λ, the wider Δy
③The farther the screen distance L, the wider Δy
④That is why the fringes of red light, with its long wavelength, are farther apart than those of violet light, with its short wavelength
⑤In the picture L is fixed, so λ/d in the top line is proportional to Δy

Single-Slit Diffraction

3
Dark-Fringe Condition for a Single Slit
a sin θ = mλ (m = ±1, ±2, …)
The direction of the m-th dark fringe for a slit of width a

Comparison

Double-Slit Interference and Single-Slit Diffraction
ItemDouble-Slit InterferenceSingle-Slit Diffraction
Sources2 (two slits)Many points within one slit
Bright fringesPath diff = mλThe center is brightest and widest
Dark fringesPath difference = (m + ½)λa sin θ = mλ
Pattern shapeEvenly spaced bandsWide center, narrower and dimmer to the sides
Real observationInterference bands seen inside a diffraction envelopeOnly the diffraction pattern
🌈 Interference and Diffraction in Everyday Life
①The rainbow colors of a soap bubble come from interference of light reflected from the front and back of a thin film
②The rainbow colors on a CD or DVD come from its closely spaced grooves acting as a diffraction grating
③The rainbow colors of an oil film on a puddle are also the result of interference between light reflected from its two surfaces
④All these effects support the idea that light is a wave

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?
1
Use the fringe spacing formula Δy = λL/d.
Δy = λLd
2
Substitute λ = 6 × 10⁻⁷ m, L = 2 m and d = 2 × 10⁻⁴ m.
Δy = 6×10-7 × 22×10-4 = 6×10-3 m = 6 mm
▸ 6 mm
Converting to meters comes first. After changing 600 nm to 6 × 10⁻⁷ m and 0.2 mm to 2 × 10⁻⁴ m, the fringe spacing comes out as 6 mm.
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?
1
In Δy = λL/d, with d and L unchanged, Δy is proportional to λ.
Δy ∝ λ (d, L fixed)
2
Use the ratio of the wavelengths directly.
ΔyvioletΔyred = 400700 = 47
▸ 4/7
The fringe spacing is proportional to the wavelength, so the fringes of violet light, with its shorter wavelength, are closer together than those of red light.

Summary

Key Formulas
d sin θ = mλ, Δy = λLd
The double-slit bright-fringe condition and the fringe spacing
CSAT-style problem, adapted
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×
1
The fringe spacing Δy = λL/d is inversely proportional to the slit spacing d.
Δy = λLd
2
If d becomes 2 times larger, Δy becomes 1/2 as large.
d→2d ⇒ Δy ∝ 12d = 12Δy
🎯 Exam Points
①Constructive: d sin θ = mλ gives a bright fringe (path difference = whole number of wavelengths)
②Destructive: d sin θ = (m + ½)λ gives a dark fringe
③The fringe spacing Δy = λL/d is wider when d is smaller and when λ and L are larger
④Dark fringes of a single slit: a sin θ = mλ
⑤Interference and diffraction are evidence of the wave nature of light, and the photoelectric effect is evidence of its particle nature
← Previous
Electromagnetic Induction
Next →
Matter Wave and Uncertainty Principle

Last updated

Was this helpful? Support seegongsik