Diffraction
High-Yield Summary
- Diffraction: light spreads out passing through a narrow opening or around an obstacle — a wave-nature effect, most pronounced when slit width ≈ wavelength.
- Single-slit dark fringes: a sinθ = nλ (whole-integer order n = 1,2,3…).
- Young's double-slit: two slits' diffracted waves interfere — constructive (in phase) → bright maxima; destructive (out of phase) → dark minima.
- Double-slit dark fringes use a half-integer order: d sinθ = (n + ½)λ — different from single-slit's whole-integer formula. Double-slit bright fringes: d sinθ = nλ.
- A diffraction grating (many regularly spaced slits) separates wavelengths via interference — visually similar to a prism, but prisms separate color by refraction, gratings by interference.
Single-Slit Dark Fringes
a sinθ = nλ
- a = Slit width
- θ = Angle from slit center to the point of minimum intensity
- n = Integer fringe order (1, 2, 3, …)
- λ = Wavelength of incident light
- Narrower slit → wider central maximum and more spread-out fringe pattern.
Double-Slit Fringe Formulas
| Fringe type | Formula |
|---|---|
| Bright fringes (maxima) — constructive | d sinθ = nλ (whole-integer order) |
| Dark fringes (minima) — destructive | d sinθ = (n + ½)λ (half-integer order) |
Common MCAT Trap
- Single-slit dark fringes use whole-integer order (a sinθ = nλ); double-slit dark fringes use half-integer order (d sinθ = (n+½)λ) — mixing these up is the classic MCAT trap on this topic.
- A diffraction grating separates color through interference, not refraction — don't describe it using prism-style refraction reasoning.
Quick Recall
In a double-slit setup, is d sinθ = 2λ a bright or dark fringe?
Why does narrowing a single slit widen the central maximum?