lens power

Meaning: Lens power measures how strongly a lens bends light. A lens with a short focal length bends rays sharply, so its power is large. Converging (convex) lenses have f > 0 and positive power. Diverging (concave) lenses have f < 0 and negative power. Thin lenses placed in contact add their powers.

Equation: P = 1/f, and for thin lenses in contact Ptotal = P₁ + P₂. P is power in diopters (D = m⁻¹) and f is focal length in meters. The thin-lens equation 1/f = 1/o + 1/i links power to object distance o (m) and image distance i (m).

On the MCAT: A passage gives a focal length, often in cm, and asks for the power in diopters. Another common setup is a vision problem. In a nearsighted eye the image forms in front of the retina, so a diverging lens with negative power corrects it. A farsighted eye needs a converging lens with positive power. Questions also ask you to predict that accommodation makes the eye's lens thicker, which increases its power for near objects. Combined-lens questions ask you to add the diopters.

Common confusion: Lens power is not power in watts (energy per time). Students also forget to convert cm to m. A lens with f = 20 cm = 0.20 m has P = +5 D, not 0.05 D. Keep the sign, because a negative f gives a negative power.