Light behaves both as a wave (interference, diffraction, polarisation) and as a stream of photons (absorption, emission, the photoelectric effect)

Wave: speed = frequency × wavelength (c = fλ). The frequency is fixed by the source; speed and wavelength fall in a denser medium
Photon energy E = hf: shorter wavelengths carry more energy per photon, which is why UV causes photochemical damage

Physical optics deals with light as a wave. Geometric optics treats it as rays, which works when apertures are large compared with the wavelength

## The electromagnetic spectrum and the eye

Band	Wavelength	Where it is absorbed, and its effects
UV-C	100–280 nm	Cornea. Excimer laser (193 nm) ablates the corneal surface
UV-B	280–315 nm	Mainly the cornea: photokeratitis (snow blindness, welder's flash), pterygium. Some reaches the lens: cortical cataract
UV-A	315–400 nm	Mainly the adult lens. Children's lenses transmit more UV to the retina. Aphakia removes this filter, hence UV-blocking IOLs
Visible	about 400–700 nm	Transmitted to the retina. Peak photopic sensitivity 555 nm, scotopic 507 nm. Blue light (around 440 nm) carries the greatest photochemical retinal hazard (solar retinopathy)
IR-A	700–1400 nm	Reaches the retina, so it is a thermal retinal hazard. Nd:YAG (1064 nm) and diode (810 nm) lasers
IR-B and IR-C	over 1400 nm	Absorbed by water in the cornea and aqueous. Near infrared (IR-A and IR-B) absorbed by the iris and lens causes glassblower's cataract (true exfoliation of the lens capsule)

## Measuring light

Radiometry measures all radiant energy (watts). Photometry weights it by the eye's sensitivity

Luminous flux: lumen
Luminous intensity of a point source: candela (lumens per steradian)
Illuminance, the light falling on a surface: lux (lumens per m²)
Luminance, the brightness of a surface: cd/m². Perimetry backgrounds and stimuli are set in cd/m² or apostilbs

Worked example: moving a reading lamp from 1 m to 50 cm increases the illuminance on the page 4 times (1 ÷ 0.5² = 4)
Cosine law: light striking a surface obliquely spreads out, so illuminance = I cos θ ÷ d²

## Interference

In phase (path difference a whole number of wavelengths): constructive interference, brighter
Half a wavelength out of phase: destructive interference, cancellation

Anti-reflection coatings: a layer a quarter of a wavelength thick, so light reflected from its two surfaces cancels. The ideal coating index is √n of the lens. An uncoated surface reflects about 4% for n = 1.5, more for high-index materials
OCT and optical biometry: low-coherence (partial coherence) interferometry measures the depth of reflecting layers (see Optical Coherence Tomography and Biometry)
Interference filters, and laser interferometers that project fringes onto the retina to estimate potential acuity behind a cataract

## Diffraction and resolution

Waves bend at the edges of an aperture. A point source imaged through a circular aperture becomes a bright central disc with faint rings: the Airy disc
Rayleigh criterion: two points are just resolved when the centre of one Airy disc falls on the first dark ring of the other

Minimum angle of resolution θ = 1.22λ ÷ d (radians), where d is the aperture diameter
Smaller pupils cause more diffraction; larger pupils cause more aberration
Worked example: for a 3 mm pupil and λ = 555 nm, θ = 1.22 × 555×10⁻⁹ ÷ 0.003 = 2.3×10⁻⁴ rad ≈ 0.8 minute of arc, just below the 1 minute of 6/6 acuity

Pinhole: improves acuity in refractive error by increasing depth of focus. A hole of about 1.2 mm works best; smaller holes lose acuity to diffraction and dimness
Diffractive multifocal and EDOF IOLs use diffraction rings to split light between foci, at the cost of contrast and halos

## Polarisation

Light is a transverse wave. In unpolarised light the vibrations are in all planes perpendicular to the ray; in plane-polarised light they are in one plane
Polarisation by

Absorption: polarising (Polaroid) filters
Reflection: reflected light is fully polarised at Brewster's angle, where tan θ = n (about 56° for glass, n = 1.5)
Birefringent (doubly refracting) materials, e.g. the Wollaston prism (see Prisms)

Polarising sunglasses: glare reflected from water and roads is horizontally polarised, so a vertical transmission axis blocks it
Stereotests with polarised vectographs (Titmus, Randot)
Scanning laser polarimetry: the retinal nerve fibre layer is birefringent, so its retardation estimates RNFL thickness
Haidinger's brushes: an entoptic image from the radially arranged macular pigment, used in pleoptics and to test macular function

## Scattering and fluorescence

Rayleigh scattering by particles much smaller than the wavelength is proportional to 1/λ⁴: blue (450 nm) is scattered about 6 times more than red (700 nm). Hence the blue sky and blue irides
Mie scattering by larger particles (cataract, corneal oedema, scars) is roughly independent of wavelength and causes glare. The Tyndall effect of AC flare is scatter from protein
Fluorescence: a molecule absorbs light and re-emits it at a longer wavelength (lower energy)

Fluorescein absorbs blue light (peak about 490 nm) and emits yellow-green (about 520–530 nm). The cobalt blue excitation filter and a yellow barrier filter make it visible
Indocyanine green absorbs and emits in the near infrared (about 805 and 835 nm), which passes through RPE and blood, so it shows the choroid

## Coherence and lasers

Laser light is monochromatic, coherent (in phase in time and space), collimated and very intense
It is produced by stimulated emission in a pumped medium with a population inversion. A resonant cavity between a full mirror and a partially transmitting mirror amplifies it

Laser physics, the laser types and their tissue effects (photocoagulation, photodisruption, photoablation) are covered in the LASERs note.