How this instrument works
Optical power answers one blunt question: how hard does this piece of glass bend light? Short focal lengths bend hard, so strength is defined as their reciprocal, one dioptre meaning one reciprocal metre. Choosing that inverted scale buys something raw focal lengths cannot offer — additivity. Press two thin lenses together and their dioptres simply sum, +2.00 alongside +0.50 giving +2.50, where 500 mm and 2000 mm would demand reciprocal arithmetic for every trial pair. An optometrist flicking glass into an empty frame is working no harder than that.
Ferdinand Monoyer — French ophthalmologist, better remembered for hiding his own surname down two columns of an eye chart — proposed this unit in 1872. Its name descends from dioptra, a Greek sighting instrument, by way of Kepler's Dioptrice of 1611. Clinical practice adopted it within ten years and has not budged since. Magnitudes worth carrying in your head: relaxed human eyes total roughly 60 D, drugstore readers run +1.00 to +3.50, short-sight corrections cluster between −0.50 and −6.00, and jeweller's loupes reach 40 D. Prescriptions step in quarter-dioptre increments because that is about where patients stop noticing any change at all.
P = 1 ⁄ f describes an idealised thin element working close to its axis. Give real glass thickness and its strength depends on both surface curvatures plus refractive index, through lensmaker's arithmetic carrying its own t ⁄ n correction. Separate two elements by a gap d and additivity acquires a subtraction, P = P₁ + P₂ − d·P₁·P₂, which is why telescopes are more than their objectives plus their eyepieces. Shift spectacles 12 mm off the cornea and effective strength moves too, noticeably past ±4 D. Submerge anything in water and everything scales with surrounding index, since what curved surfaces truly alter is vergence, n ⁄ distance, rather than distance alone.
- Enter Focal length in whichever unit your glass is marked in — millimetres for camera optics, centimetres for magnifiers, metres for spectacle work.
- Keep the sign. Converging elements take positive focal lengths, diverging ones negative, and Optical power (dioptres) inherits whichever you give.
- Read Optical power (dioptres) straight off. Six decimals are shown, though clinics round to quarters and photographers to whole numbers.
- Zero is refused: Focal length must not be zero. Flat window glass sits at an opposite extreme — infinite focal length, and a power of precisely 0 D.
- Going backwards is one keystroke of mental arithmetic: f = 1 ⁄ P, so a −2.50 prescription describes a focal length of −0.4 m, or 400 mm.
Worked example — the lens that defines the unit
Take the weakest pair off any rack of ready-made readers, marked +1.00. Hold one eyepiece up to bright daylight and slide white paper behind it until some distant rooftop snaps into one small inverted image; tape measure puts that paper 1.00 metre back. Enter 1 into Focal length with its unit set to m. Optical power (dioptres) returns 1. No rounding, no constant, no fudge — that identity is the definition of one dioptre, and every other figure on this scale hangs off it.
Proportion handles all the rest. Halve that focal length to 0.5 m and strength doubles to 2 D; 50 mm portrait glass, being one twentieth of one metre, arrives at 20 D. Photographers seldom speak this language out loud, yet close-up attachment filters are sold in it — +4 marks 250 mm of focal length screwed onto your front thread, and adding +2 behind gives 6 D, or about 167 mm.
Questions
Why is a 50 mm lens 20 dioptres rather than 0.02?
Because inversion happens in metres, and 50 mm is 0.05 m — one over 0.05 gives 20. Dividing 1 by 50 answers a different question, returning strength per millimetre, and it is the single commonest slip with this formula. Picking mm from the unit menu handles conversion for you. Sanity check: anything focusing shorter than a metre must exceed 1 D, and anything under 100 mm must exceed 10 D.
What does a negative dioptre value mean?
A diverging element — concave, thinner through its middle, spreading a parallel beam instead of gathering it. Its focus is virtual, sitting on the same side as incoming light, so focal length carries a minus sign and strength inherits it. Short-sightedness is corrected with negative figures, long-sightedness and reading adds with positive. A prescription reading −3.25 describes a focal length of −0.3077 m.
Do two lenses held together really just add?
In contact and thin, yes, and that additivity is the whole reason this unit exists. Pull them apart by a gap d in metres and a cross term appears: P = P₁ + P₂ − d·P₁·P₂. Two +5 D elements touching make +10 D; that same pair 40 mm apart make 9 D. Optometrists lean on the touching case constantly while stacking trial glass, whereas lens designers live entirely in the separated one.
How many dioptres is a human eye?
About 60 D relaxed. That looks impossible against a 24 mm eyeball until you notice image space is vitreous humour at index 1.336, and strength inside a medium is n ⁄ f rather than 1 ⁄ f. Roughly 43 D of it belongs to the air-cornea boundary, where the biggest index jump happens; a crystalline lens supplies about 19 D and flexes for more. Accommodation range falls from near 14 D in a child to under 2 D by the mid-fifties — presbyopia, and the reason readers sell by the million.
Why do glasses and contacts need different prescriptions?
Vertex distance. Spectacles ride roughly 12 mm ahead of a cornea, contacts sit directly on it, and sliding an element along an axis changes where its focus lands relative to a retina. Effective strength is P ⁄ (1 − d·P) with d in metres: a −8.00 spectacle becomes about −7.30 as a contact, a +8.00 becomes +8.85. Below roughly ±4 D that shift stays inside one quarter-dioptre step and gets ignored; above it, dispensing opticians compensate every single time.
Is the dioptre an SI unit?
Not strictly. It is a special name for a reciprocal metre, m⁻¹, listed by BIPM among accepted non-SI units rather than inside any coherent SI table. Writing 2.5 m⁻¹ instead of 2.50 D would be dimensionally impeccable and clinically bewildering, so ophthalmology keeps its own word. Prism strength is quoted separately, in prism dioptres, measuring sideways deviation of one centimetre at one metre — a wholly different quantity that unfortunately shares a name.