Wave Interference

Interference arises when two coherent waves overlap. Young's double-slit experiment demonstrates the wave nature of light, producing bright fringes where waves add constructively and dark fringes where they cancel.

Key Concepts

Constructive interference: path difference = mλ
Destructive interference: path difference = (m+½)λ
Young's double slit: fringe spacing Δy = λL/d
Thin-film interference accounts for phase shifts at boundaries
Coherence required for stable interference patterns

Key Equations

Bright fringes (double slit)

d\sin\theta = m\lambda,\quad m=0,\pm1,\pm2,\ldots

Fringe spacing

\Delta y = \frac{\lambda L}{d}

Thin film (air between plates)

2t = m\lambda\text{ (constructive, one phase-flip)}

Michelson path difference

\Delta = 2d

Worked Example

Example Problem

Problem

In Young's double-slit experiment, λ=550 nm, d=0.25 mm, L=1.5 m. Find the fringe spacing.

Solution

Δy = λL/d = 550×10⁻⁹ × 1.5 / 0.25×10⁻³ = 3.30×10⁻³ m = 3.30 mm.

Practice

Exercises

7 problems

1 of 7

Double-slit: λ=600 nm, d=0.30 mm, L=2.0 m. Find fringe spacing Δy in mm.

Your answer

2 of 7

Double-slit: λ=500 nm, d=0.20 mm, L=1.0 m. Find the position of the third bright fringe (m=3) in mm from center.

Your answer

3 of 7

A thin air wedge between glass plates shows bright fringes every 1.2 mm with λ=600 nm. How fast does the thickness increase per mm of position?

Unlock Exercise 3