C.3 Wave phenomenaIB Physics HL: Revision notes

A wavefront joins points in phase; a ray is perpendicular to the wavefronts and shows the direction of energy transfer. At a boundary a wave is partly reflected and partly transmitted; the transmitted wave is refracted if its speed changes. Frequency is unchanged, so wavelength changes with speed. Wavefront–ray diagrams show closer wavefronts in the slower medium, with the ray bending towards the normal.

$\frac{n_1}{n_2} = \frac{\sin\theta_2}{\sin\theta_1} = \frac{v_2}{v_1}$, with angles measured from the normal. Going from a higher to a lower refractive index, the critical angle c satisfies sin c = n₂/n₁. For angles of incidence above c, total internal reflection occurs and no light is transmitted.

Diffraction is spreading through an aperture or around an obstacle; it is strongest when the size is comparable to λ. By the principle of superposition, displacements add where waves meet. Coherent sources (constant phase difference) give stable interference: constructive when path difference = nλ, destructive when path difference = (n + ½)λ. Young's double slit gives fringes of separation $s = \frac{\lambda D}{d}$.

Light passing through a single slit of width b gives a broad, bright central maximum with much weaker side maxima. The first minimum is at angle $\theta = \frac{\lambda}{b}$ (in radians, small angle). The central maximum is twice as wide as each side maximum, and its angular half-width grows as λ increases or b decreases. Minima occur because waves from different parts of the slit cancel in pairs.

Each slit of a real double slit has a width b, so the double-slit fringes (spacing λD/d) lie under a single-slit envelope (first minimum at λ/b). The fringes are brightest near the centre and fade outwards. Where an interference maximum falls at a single-slit minimum, it is missing, because neither slit sends light in that direction. The number of fringes in the central envelope depends on d/b: if d/b = 5, the fifth order is missing and 9 fringes lie in the central maximum.

With N slits, maxima occur at the same angles as for two slits with the same spacing, $n\lambda = d\sin\theta$, but they are much brighter (more slits contribute) and much sharper (slightly away from a maximum, waves from slits across the grating cancel). A grating with N lines per metre has d = 1/N. The highest order satisfies n ≤ d/λ because sin θ cannot exceed 1. Gratings are used to measure wavelengths precisely and to separate close spectral lines.