Refraction: the change in direction of light as it passes obliquely from one medium into another, because its speed changes
Refractive index n = speed of light in a vacuum ÷ speed in the medium (n of air ≈ 1)

A higher n is an optically denser medium, in which light travels more slowly
n varies with wavelength (dispersion): it is higher for blue than for red light

Medium	Refractive index
Air	1.000
Water	1.333
Aqueous and vitreous	1.336
Cornea	1.376
Crystalline lens	1.386 (cortex) to 1.406 (nucleus)
Silicone oil	about 1.40
PMMA	1.49
CR39 (spectacle plastic)	1.498
Crown glass	1.523
Polycarbonate	1.586
High-index plastics and glass	1.6–1.9

## Snell's law

n₁ sin i = n₂ sin r, where i and r are measured from the normal

So sin i ÷ sin r = n₂ ÷ n₁
Into a denser medium, light bends towards the normal. Into a less dense medium, it bends away from it
Light striking a surface along the normal is not deviated

Worked example: light in air meets glass (n = 1.5) at 30° to the normal. sin r = sin 30° ÷ 1.5 = 0.333, so r = 19.5°

## Critical angle and total internal reflection

Going from a denser into a less dense medium, the refracted ray bends away from the normal. At the critical angle c it runs along the surface (r = 90°)

sin c = n₂ ÷ n₁ (n₁ is the denser medium)
Glass to air (n = 1.5): c = 41.8°
Cornea to air (n = 1.376): c = 46.6°

Beyond the critical angle, all the light is reflected: total internal reflection (TIR)
TIR is used in reflecting prisms (see Prisms) and in optical fibres in endoscopes and endolaser probes

The angle cannot be seen directly: light from the angle strikes the tear–air interface beyond the critical angle (about 46–49°, depending on the index used) and is totally internally reflected back into the eye. A gonioscopy lens replaces that interface with one of a similar refractive index, so the light can leave the eye (see Gonioscopy).

## Apparent depth

An object in a denser medium, viewed from above, appears closer to the surface than it is

Real depth ÷ apparent depth = n (for near-normal viewing)
Worked example: a stone 3 cm under water appears 3 ÷ 1.333 = 2.25 cm deep

In the same way, the iris and anterior chamber look shallower through the cornea than they really are

## The power of a refracting surface

A curved surface between two media refracts light like a lens

F = (n₂ − n₁) ÷ r, with r in metres. It is positive when the surface is convex towards the incoming light and n₂ is greater than n₁

Worked example: the cornea

Anterior surface, r = 7.7 mm: (1.376 − 1) ÷ 0.0077 = +48.8D
Posterior surface, r = 6.8 mm, from cornea into aqueous: (1.336 − 1.376) ÷ 0.0068 = −5.9D
Total about +43D. Keratometers use a single surface with a "keratometric index" of 1.3375 to allow for the posterior surface: 0.3375 ÷ 0.0077 = +43.8D (see keratometry)

Because power depends on the difference in refractive index, the same lens has a different power in a different medium

Underwater: water (1.333) is almost the same index as the cornea, so the anterior corneal surface loses almost all its power (about +5.6D instead of +48.8D). The eye becomes highly hypermetropic. A diving mask restores an air interface
IOLs: a PMMA IOL (1.49) is about three times stronger in air than in aqueous, since (1.49 − 1) ÷ (1.49 − 1.336) ≈ 3.2. IOL powers are always labelled for use in the eye
Silicone oil (n about 1.40) behind a lens or IOL with a convex posterior surface reduces that surface's power, so the eye shifts towards hypermetropia. A plano-convex IOL with its flat surface facing the oil avoids this

Dispersion: the variation of n with wavelength separates white light into colours. It causes chromatic aberration and is described by the Abbe number (see Aberrations).