The whole chapter, on one desk

Laws of reflection — the incident ray, reflected ray and normal lie in one plane; angle of incidence = angle of reflection.

Centre of curvature (C) / radius (R) — centre and radius of the sphere the mirror is cut from. Pole (P): centre of the mirror surface. Principal focus (F): where paraxial rays parallel to the axis converge (concave) or appear to diverge from (convex).

Plane mirror — image is virtual, erect, same size, as far behind as the object is in front, laterally inverted.

Refractive index — n = c/v, a measure of optical density. Frequency is fixed at a boundary; speed and wavelength both fall by n. Relative index n₂₁ = n₂/n₁ = v₁/v₂ = λ₁/λ₂.

Critical angle (θc) — the angle of incidence in the denser medium for which the refracted ray grazes the surface (r = 90°). Total internal reflection: beyond θc, all light is reflected back — the basis of optical fibres and the sparkle of diamond.

Apparent depth — an object in a denser medium looks nearer the surface; lateral shift is the sideways offset of a ray leaving a parallel slab (it emerges parallel to its original path).

Angle of deviation (δ) — the turn between incident and emergent rays. As i increases, δ falls to a minimum δm then rises; at δm the passage is symmetric (i₁ = i₂, r₁ = r₂ = A/2) and the ray inside runs parallel to the base.

Dispersion — a prism spreads white light because n is larger for shorter wavelengths, so violet deviates most, red least. Dispersive power (ω) measures the spread relative to the mean deviation. Cauchy: n = A + B/λ². Spectra: continuous (hot solids), line (atoms), band (molecules), absorption (dark Fraunhofer lines); a spectrometer (collimator · prism table · telescope) reads A and δm to get n(λ).

Thin lens — two refracting surfaces a negligible distance apart. Beyond 2F: real, inverted, small; between F and 2F: real, inverted, large; inside F: virtual, erect, magnified (the magnifier).

Power (P) — P = 1/f in dioptres (f in metres); converging +, diverging −. In contact, powers add.

Silvered lens — a lens with one face mirrored behaves as an equivalent mirror; the lens power counts twice. Displacement method: a lab way to get f from the two sharp positions of a lens between a fixed object and screen (needs D > 4f).

Chromatic aberration — f is shorter for violet than red, so white light focuses over a stretch of axis. Longitudinal CA = f_r − f_v = ω f. An achromatic doublet (converging crown + diverging flint, cemented) cancels it: ω₁/f₁ + ω₂/f₂ = 0.

Wavefront — a surface of constant phase. Huygens’ principle: every point on a wavefront is a source of secondary wavelets; their envelope is the next wavefront.

Coherent sources — constant phase difference (needed for a steady interference pattern). Path difference (Δ): the extra distance one wave travels — whole λ give brightness, half-λ give darkness.

Diffraction — bending of light into the geometric shadow of an edge or slit. Resolving power: ability to see two close objects as separate (Rayleigh criterion).

Polarisation — restricting the light’s vibration to one plane — proof light is a transverse wave. Brewster angle: incidence at which the reflected ray is fully plane-polarised.

Magnifying power — ratio of the angle an image subtends at the eye to the angle the object would subtend unaided (at D = 25 cm). Every instrument is angle inflation.

Near / far point — closest (25 cm) and farthest (∞) points of clear vision for a normal eye; accommodation is the lens reshaping to focus both.

Myopia (short sight) — distant objects blur; the eyeball is too long; corrected with a concave lens (f = −far point). Hypermetropia (long sight) — near objects blur; eyeball too short; corrected with a convex lens.