Waves, Sound and Geometric Optics
Scope of the domain
This domain covers wave properties, stationary waves and sound, and the refraction and imaging rules of geometric optics. The exam asks you to use v = fλ, analyse nodes and antinodes, apply Snell's law and critical-angle conditions, and calculate image position and magnification for lenses.
Core rules
- Wave speed v = fλ; frequency is set by the source and does not change when a wave enters a new medium, but speed and wavelength do.
- Transverse waves oscillate perpendicular to the direction of travel; longitudinal waves, including sound, oscillate parallel to it.
- Superposition adds displacements. Stationary waves have nodes (zero amplitude) and antinodes (maximum amplitude), separated by half a wavelength.
- String fixed at both ends: fₙ = nv/(2L), with n = 1, 2, 3… Open pipe: fₙ = nv/(2L). Pipe closed at one end: fₙ = nv/(4L) for odd n only.
- Echo ranging: total distance = v × t, so the distance to the reflector is vt/2.
- Refraction: n₁ sinθ₁ = n₂ sinθ₂; refractive index n = c/v. Total internal reflection occurs only from denser to less dense medium, when the angle exceeds the critical angle sinC = n₂/n₁.
- Thin lens: 1/f = 1/u + 1/v; magnification m = v/u. A real image is formed by converging rays and can be projected; a virtual image cannot.
Worked example
An object is placed 30 cm from a convex lens of focal length 10 cm. Using 1/f = 1/u + 1/v: 1/10 = 1/30 + 1/v, so 1/v = 1/10 − 1/30 = 2/30 and v = 15 cm. The image is real, inverted and on the opposite side of the lens. Magnification m = v/u = 15/30 = 0.50, so the image is half the object's height.
Traps that cost marks
- Changing the frequency when light refracts; only speed and wavelength change.
- Confusing nodes with antinodes, or counting the wrong number of half-wavelengths in a pipe.
- Using the closed-pipe formula for an open pipe, or allowing even harmonics in a closed pipe.
- Forgetting that total internal reflection requires the wave to travel towards a less dense medium.
- Mixing degrees and radians in Snell's law calculations.
- Sign errors in the lens equation, especially for virtual images where v is negative.