Double Slit & Diffraction
A short lesson with diagrams, a worked example, a problem to try, and a quick check. Then quiz yourself on 6 practice questions.
Light passing through two narrow slits spreads out and overlaps. Where the two paths differ by a whole number of wavelengths, the waves add: a bright fringe. Where they differ by a half wavelength, they cancel: a dark fringe. This proves light is a wave.
1. The double-slit pattern
2. Diffraction
Single slit: light spreads into a wide central band with dimmer bands beside it. A narrower slit spreads the light more, so the central band gets wider.
Diffraction grating: thousands of slits make very sharp, bright lines at d sin θ = mλ. Red light (longer λ) bends more than blue.
Thin films (soap bubbles, oil on water): light reflecting off the front and back surfaces interferes. Which colors add up depends on the film’s thickness, so you see swirling colors.
Bigger λ or L spreads the fringes; bigger d squeezes them together.
3. Example, then try it
Light of wavelength 600 nm passes through two slits 0.20 mm apart onto a screen 1.5 m away. Find the fringe spacing.
Δy = λL/d = (600 × 10⁻⁹)(1.5) ÷ (0.20 × 10⁻³) = 4.5 × 10⁻³ m = 4.5 mm.
A diffraction grating has 500 lines per millimeter. Find the angle of the first-order line for red light (650 nm) and for blue light (450 nm). What is the highest order of red light you can see?
Slit spacing: d = 1 mm ÷ 500 = 2.0 × 10⁻⁶ m.
Red, m = 1: sin θ = 650 × 10⁻⁹ ÷ 2.0 × 10⁻⁶ = 0.325, so θ ≈ 19°.
Blue, m = 1: sin θ = 0.225, so θ ≈ 13°. Red bends more.
Highest red order: sin θ can’t exceed 1, so m ≤ d/λ = 3.08. The highest is m = 3.
Answer: red 19°, blue 13°; red up to third order.
4. Common mistakes
A double-slit experiment is repeated with a longer wavelength of light. What happens to the fringes?
Δy = λL/d. A longer wavelength gives a larger fringe spacing.
Ready to practice?
6 questions on Double Slit & Diffraction, each with a hint and an explanation for every wrong answer.