C.3 Wave phenomenaIB Physics SL: Revision notes

A wavefront is a line (in 2D) or surface (in 3D) joining points that are in phase, such as all the crests. A ray shows the direction in which the wave's energy travels and is always perpendicular to the wavefronts. The distance between adjacent wavefronts drawn at crests is one wavelength. Plane waves have straight, parallel wavefronts; a point source produces circular (2D) or spherical (3D) wavefronts.

When a wave reaches a boundary between two media, some energy is reflected, some is transmitted into the new medium, and the transmitted wave is usually refracted (changes direction) because its speed changes. The frequency never changes at a boundary, since it is set by the source, so a change of speed means a change of wavelength ($v = f\lambda$). Waves slowing down bend towards the normal; waves speeding up bend away from the normal. On a wavefront–ray diagram, the wavefronts in the slower medium are closer together and turn so that the part that entered first lags behind.

Snell's law: $\frac{n_1}{n_2} = \frac{\sin\theta_2}{\sin\theta_1} = \frac{v_2}{v_1}$, where θ is measured from the normal and refractive index n = c/v. The angle between a wavefront and the boundary equals the angle between the ray and the normal.

When light travels from a higher to a lower refractive index, the angle of refraction reaches 90° at the critical angle c, where sin c = n₂/n₁. For angles of incidence greater than c there is total internal reflection: no light is transmitted. Optical fibres use this, with a core of higher index than the cladding.

Diffraction is the spreading of a wave as it passes through an aperture or around the edge of an obstacle. The effect is most noticeable when the aperture or obstacle size is comparable to the wavelength; when the gap is many wavelengths wide the wave passes almost straight through with a sharp shadow. Wavelength and speed are unchanged by diffraction. This is why sound (wavelengths of metres) is heard round corners, while light (about 5 × 10⁻⁷ m) casts sharp shadows.

The principle of superposition: where two waves or pulses meet, the resultant displacement is the vector sum of the individual displacements; afterwards they continue unchanged. For a stable interference pattern from two sources, the sources must be coherent (same frequency, constant phase difference).

For two sources in phase:

• constructive interference when path difference = nλ
• destructive interference when path difference = (n + ½)λ

Light from one coherent source (a laser) passes through two narrow slits a distance d apart; the slits diffract the light and the overlapping waves interfere on a screen a distance D away, giving equally spaced fringes with separation $s = \frac{\lambda D}{d}$. Increasing λ or D spreads the fringes; increasing d squeezes them together. Measuring s, d and D gives the wavelength of light.