A person with myopia can see objects clearly only up to a distance of 2 m. What power of lens is needed to correct this defect? Explain why this lens works.

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MYOPIA: The person cannot see objects farther than 2 m (far point = 2 m). The lens must bring the image of a very distant object (at infinity, u = ∞) to the far point (v = −2 m, negative because virtual image is on same side as object for corrective lens). Using lens formula: 1/v − 1/u = 1/f. 1/(−2) − 1/∞ = 1/f. −0.5 − 0 = 1/f. f = −2 m. POWER: P = 1/f = 1/(−2) = −0.5 D. A CONCAVE lens of power −0.5 D (or 0.5 D, concave). WHY IT WORKS: A myopic eye is too converging (the eyeball is elongated or the lens is too thick). A concave lens DIVERGES the incoming rays, making them appear to come from the far point (2 m). The eye then converges these diverging rays normally onto the retina, giving a clear image.

Practice — Refraction of Light at Plane Surfaces

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