Physical optics (interference & diffraction)
The idea
Geometric optics treats light as rays, but rays cannot explain why two beams can add to darkness. Physical optics restores the wave picture: when light from two coherent sources overlaps, the fields superpose, and the result depends on the path difference. Where the paths differ by a whole number of wavelengths the waves arrive in phase and reinforce (bright fringe); where they differ by a half-integer number they cancel (dark fringe). Young's double slit turns this into a measuring instrument for the wavelength of light itself.
For slits separated by d and a screen far away, bright fringes appear where d sinθ = mλ for integer m, and for small angles the fringes are evenly spaced on the screen by Δy = λL/d. Diffraction is the same superposition story applied to the continuum of points across a single opening: a slit of width a throws minima at a sinθ = mλ, and narrower openings spread light more — the ultimate limit on how finely any optical instrument can resolve.
The geometry inverts naive intuition: shrinking the slit spacing or the slit width makes the pattern wider, not narrower, because smaller d demands a larger angle to accumulate one wavelength of path difference. Interference effects hide in daily life only because visible wavelengths are sub-micrometer and ordinary sources lack coherence — not because the physics is exotic.
Worked example
Laser light of wavelength 633 nm passes through two slits separated by 0.25 mm, and the pattern falls on a screen 2.0 m away. Find the spacing between adjacent bright fringes and the distance from the central maximum to the third-order bright fringe.
- Check the small-angle regime: the first maximum sits at sinθ = λ/d = (633 × 10⁻⁹)/(2.5 × 10⁻⁴) ≈ 2.5 × 10⁻³, a fraction of a degree, so sinθ ≈ tanθ and the linear fringe formula applies.
- Compute the fringe spacing: Δy = λL/d = (633 × 10⁻⁹ × 2.0)/(2.5 × 10⁻⁴) = 5.1 × 10⁻³ m ≈ 5.1 mm.
- Locate the third bright fringe: maxima are equally spaced in this regime, so y₃ = 3Δy ≈ 15.2 mm from the central maximum.
- Interpret the mechanism: at y₃ the light from one slit travels exactly 3 wavelengths (about 1.9 μm) farther than from the other, so the crests still arrive together and reinforce.
- Sanity-check the leverage: a quarter-millimeter slit spacing converted a 633 nm wavelength into millimeter-scale fringes — magnification by roughly L/d ≈ 8000 — which is precisely how such experiments first measured the wavelength of light.
Answer. Adjacent bright fringes are about 5.1 mm apart, putting the third-order bright fringe about 15 mm from the center.
Check your understanding
- Why does decreasing the slit separation spread the fringes farther apart rather than closer together?
- What does the requirement of coherence mean physically, and why do two separate flashlights not produce visible fringes?
- How does single-slit diffraction modify the ideal double-slit pattern you would calculate from two point sources?
- Where does the energy go at the dark fringes if light plus light yields darkness there?
Build the foundations first
Physical optics (interference & diffraction) builds on these concepts. If any feel shaky, start there.