A prism is a transparent medium bounded by two plane surfaces inclined to each other

The angle between the two surfaces is the refracting angle (apical angle, α)
The thickest part, opposite the apex, is the base

Light is refracted at both surfaces and is always deviated towards the base
The image is virtual, erect and displaced towards the apex: the eye projects the emerging ray straight back

## Angle of deviation

The angle of deviation (D) depends on

The refractive index of the prism material (n)
The refracting angle (α)
The angle of incidence

Deviation is least when light passes through the prism symmetrically: the position of minimum deviation
For a thin prism (refracting angle up to about 10–15°): D = (n − 1)α

For glass or CR39, n ≈ 1.5, so D ≈ α/2: a thin prism deviates light by about half its refracting angle
Worked example: a 6° crown glass prism (n = 1.52) deviates light by (1.52 − 1) × 6 ≈ 3.1°

Prisms also disperse white light, because n varies with wavelength: blue is deviated more than red (see chromatic aberration)

Prentice position: one surface of the prism is normal (perpendicular) to the incident light, so all of the deviation occurs at the opposite surface.

Glass prisms are calibrated in the Prentice position
Plastic orthoptic prisms and prism bars are calibrated in the position of minimum deviation, which is approximately the frontal plane position (back surface parallel to the patient's frontal plane)
Holding a prism in the wrong position gives an inaccurate measurement of the deviation

## The prism dioptre

Prism dioptre (Δ): the power of a prism that displaces an image 1 cm at a distance of 1 m

Prism power in Δ = 100 × tan D
1° ≈ 1.75Δ, so 1Δ ≈ 0.57°
This conversion holds for small angles only: prism dioptres grow with tan D, so 45° = 100Δ, not 79Δ
Worked example: a prism that displaces a target 6 cm at 3 m has a power of 6 ÷ 3 = 2Δ

Prism prescriptions state the power and the direction of the base (base up, down, in or out)
Two prisms in different directions (e.g. one horizontal, one vertical) combine by vector addition

Worked example: 3Δ base up + 4Δ base in = 5Δ, with the base oblique (up and in), at tan⁻¹(3/4) ≈ 37° above the horizontal

Never stack two prisms with their bases in the same direction to measure a large deviation: the second prism is no longer in its calibrated position, so the powers do not simply add. Split the prism between the two eyes, or combine a horizontal and a vertical prism.

## Prentice's rule: prism in lenses

Away from its optical centre, a lens acts as a prism
P = c × F

P: prism power (Δ)
c: decentration, the distance from the optical centre (in cm)
F: lens power (D)

Base direction

Plus lens: the base is towards the optical centre (a plus lens is two prisms base to base)
Minus lens: the base is away from the optical centre (two prisms apex to apex)

Worked example: a patient wearing +5.00D lenses looks through a point 4 mm below the optical centre. P = 0.4 × 5 = 2Δ base up
Worked example (reverse): to produce 3Δ with a +6.00D lens, decentre by c = P ÷ F = 3 ÷ 6 = 0.5 cm (5 mm)
This explains induced prism from badly centred spectacles, and the vertical imbalance on downgaze in anisometropia (see prescribing spectacles)

## Clinical uses of prisms

Measuring deviations

Prism cover test with a prism bar
Krimsky (prism reflex) test: prisms centre the corneal reflexes when a cover test isn't possible
Maddox rod, with a prism bar to neutralise the deviation (the Maddox wing reads the deviation directly off its scale)
Risley (rotary) prisms: two equal prisms rotating in opposite directions give a continuously variable power, used in phoropters to measure deviations and vergences

Measuring fusional reserves (prism vergence amplitudes)
The 4Δ base-out test for a small central scotoma (e.g. microtropia)
Relieving diplopia in decompensating phorias, small-angle strabismus and some ocular motor palsies

To correct a deviation, the prism is placed with its apex towards the direction in which the eye is deviated (base opposite):

Esotropia: base out
Exotropia: base in
Right hypertropia: base down in front of the right eye (or base up in front of the left)

Fresnel prism: a thin plastic sheet of tiny parallel prisms of identical refracting angle, giving the same overall effect as a single larger prism. It can be stuck onto a patient's glasses, so it is light and cheap and useful for temporary or changing deviations. It reduces acuity and contrast, and the ridges are visible and collect dirt.

## Prisms in optical instruments

When light inside a prism strikes a surface at an angle of incidence greater than the critical angle (about 42° for glass), it undergoes total internal reflection

A reflecting prism therefore acts as a mirror with almost no light loss and no silvering to tarnish

Prism	Effect on light	Example uses
Right-angle prism	Total internal reflection turns light through 90° and inverts the image in one meridian	Folding the light path in instruments
Porro prism	Two internal reflections return light through 180° and invert the image; a pair erects it	Binoculars, and the erecting system of slit lamp and operating microscopes
Dove prism	Inverts the image without deviating the beam; rotating it rotates the image at twice the rate	Image rotation
Wollaston prism	Splits light into two beams polarised at right angles, diverging at a fixed angle	Image doubling in some keratometers

Other instruments that use prisms

Goldmann applanation tonometer: two prisms in the head split the fluorescein ring into two semicircles (see Goldmann tonometry)
Binocular indirect ophthalmoscope: prisms or mirrors reduce the examiner's effective interpupillary distance so stereopsis is kept through a small pupil
Keratometer: a doubling prism (e.g. the Wollaston prism of the Javal–Schiøtz keratometer) lets the mires be measured despite eye movement (see keratometry)