Waves and Optics
Core concepts
Know the wave equation v = fλ, superposition, and the conditions for constructive and destructive interference (path difference of mλ and (m + ½)λ). For standing waves on strings and in pipes, identify nodes and antinodes and the harmonic series; open pipes support all harmonics, closed pipes only odd ones. In optics, apply Snell's law (n₁sinθ₁ = n₂sinθ₂), total internal reflection when going from higher to lower index beyond the critical angle, thin-lens and mirror equations (1/f = 1/d_o + 1/d_i), and the double-slit condition d sinθ = mλ. Understand polarization, dispersion, and the Doppler effect qualitatively.
Common traps
- Mixing up nodes (zero displacement) and antinodes (maximum displacement).
- Forgetting that frequency is set by the source and does not change on refraction, while wavelength does.
- Sign conventions in the lens equation; real images are inverted for a single lens.
- Applying the closed-pipe harmonic series to an open pipe.
Worked example
Light of wavelength 600 nm passes through a double slit with spacing 0.30 mm. The first-order maximum occurs at sinθ = λ/d = 600×10⁻⁹ / 3.0×10⁻⁴ = 2.0×10⁻³, so θ ≈ 0.11°. Small-angle approximations are fine here.
Rule of thumb
For standing waves, the fundamental sets the pattern: string fixed at both ends has λ = 2L; an open pipe also has λ = 2L; a closed pipe has λ = 4L.