diopter
Summary
A diopter (D) is the unit of optical power of a lens or curved mirror, equal to 1/f with f in meters (1 D = 1 m⁻¹). Shorter focal length means greater power; converging lenses are positive, diverging negative. Powers of thin lenses in contact add.
Detail
Meaning: A diopter (D) is the unit of optical power: how strongly a lens or curved mirror bends light. A shorter focal length means stronger bending and a larger magnitude of power. Converging lenses have positive power and diverging lenses have negative power. Thin lenses in contact have powers that add.
Equation: P = 1/f, where P is power in diopters (1 D = 1 m⁻¹) and f is focal length in meters (m). For thin lenses in contact, Ptotal = P₁ + P₂. It matches the thin lens equation 1/o + 1/i = 1/f, with o and i the object and image distances in meters.
On the MCAT: Vision-correction passages give a prescription in diopters and ask for a focal length or lens type. A nearsighted eye is typically corrected with a negative (diverging) lens, and a farsighted eye with a positive (converging) lens. Example: −2.0 D gives f = −0.50 m. Combined-lens questions ask you to add powers.
Common confusion: Students put f in centimeters. Convert to meters first: f = 20 cm = 0.20 m gives P = 5 D. Also, the sign shows lens type, not strength: a −4 D lens is stronger than a +2 D lens.
Sources
- Physics (Cutnell and Johnson)
- Physics: Principles with Applications (Giancoli)
Written for the MCAT and checked before it was published. For study reference only. Spotted an error? Let us know.