AP Physics 2 Physical Optics: Wave Behavior of Light

Physical optics

Branch of optics that treats light as a wave (used to explain interference and diffraction), rather than only as rays as in geometric optics.

Superposition (of waves)

When two or more waves overlap, the resulting wave is the algebraic sum of their electric fields at each point in space.

Intensity (light)

What detectors/eyes measure; proportional to the square of the wave’s amplitude (field magnitude), so interference changes brightness.

Interference pattern

Spatial pattern of bright and dark regions produced by superposition, due to varying phase differences across a screen.

Phase difference (Δφ)

How much one wave is shifted relative to another within a cycle; one full cycle corresponds to 2π radians.

Path difference (ΔL)

Difference in distances traveled by two waves to reach the same point; determines their phase difference for same wavelength in the same medium.

Phase–path relationship

For wavelength λ in a medium: Δφ = (2π/λ)ΔL.

Coherent sources

Sources that maintain a constant phase relationship over time (same frequency and stable phase difference), producing stable interference.

Constructive interference

Waves add to produce a maximum (bright) intensity; occurs when phase difference is 0, 2π, 4π… or when ΔL = mλ.

Destructive interference

Waves cancel to produce a minimum (dark) intensity; occurs when phase difference is π, 3π, 5π… or when ΔL = (m + 1/2)λ.

Order (m) in interference conditions

Integer labeling of maxima/minima conditions (e.g., ΔL = mλ for bright). Its starting value depends on the setup (e.g., double-slit bright includes m=0).

Energy redistribution in interference

Destructive interference at one location does not destroy energy; energy is redistributed so dark regions correspond to lower intensity and bright regions to higher intensity elsewhere.

Diffraction

Spreading of a wave as it passes through an opening or around an obstacle; produces patterns that are fundamentally interference patterns.

Single-slit diffraction

Diffraction from one slit where different parts of the same wavefront across the slit interfere, producing a central maximum and dimmer side maxima.

Single-slit minima condition

Dark (minimum) angles for slit width a: a sinθ = mλ, where m = 1, 2, 3, … (no central minimum).

Central maximum (single-slit)

The broad bright central region in single-slit diffraction; it is wide because the first minima occur at m=1 on either side of center.

Small-angle approximation

For small θ (far screen): sinθ ≈ tanθ ≈ θ, allowing simpler links between geometry and interference/diffraction equations.

Screen geometry relation

For a screen distance L and fringe displacement y: tanθ = y/L (and for small angles, sinθ ≈ y/L).

Diffraction-limited resolution

Fundamental limit on imaging/sharpness because a finite aperture spreads light into a diffraction pattern; smaller apertures and longer wavelengths increase spreading.

Double-slit experiment

Two slits separated by distance d produce alternating bright and dark fringes on a distant screen due to interference of the two coherent waves from the slits.

Double-slit path difference

Approximate path difference to a point at angle θ: ΔL = d sinθ.

Double-slit bright-fringe condition

Constructive interference (bright): d sinθ = mλ, with m = 0, 1, 2, … (m=0 is the central bright fringe).

Double-slit dark-fringe condition

Destructive interference (dark): d sinθ = (m + 1/2)λ, with m = 0, 1, 2, …

Double-slit fringe position/spacing (small angles)

Bright fringe position: y_m = (mλL)/d; adjacent bright spacing: Δy = (λL)/d (increases with λ or L, decreases with d).

Thin film interference

Interference between light reflected from the top and bottom surfaces of a thin layer; depends on extra travel in the film and possible phase shifts upon reflection.