A myopic person sees distant objects clearly only up to a far point of 50 cm. What is the minimum power of a lens (in dioptres) required to correct his vision so that he can see objects at infinity clearly? Assume a thin lens placed close to the eye.

Step-by-step solution

1. Recognise that for a myopic eye the far point is the farthest distance at which a clear image can be formed on the retina.
2. To correct vision, the corrective lens must form a virtual image of an object at infinity at the far point of the eye (‑0.50 m).
3. Apply the thin‑lens formula: $\frac{1}{v}=\frac{1}{f}+\frac{1}{u}$, where $u=\infty$ (object at infinity) and $v=-0.50\text{m}$ (image at far point, sign negative because it is virtual).
4. Since $\frac{1}{u}=0$, the equation reduces to $\frac{1}{v}=\frac{1}{f}$.
5. Substitute $v=-0.50\text{m}$: $\frac{1}{-0.50}=\frac{1}{f}$, giving $f=-0.50\text{m}$. The negative sign indicates a diverging (concave) lens.
6. Calculate the lens power $P$ using $P=\frac{1}{f}$ (with $f$ in metres): $P=\frac{1}{-0.50}=-2\text{D}$.

Concept tested: Correction of myopia

Published 21 August 2026 · How this solution was prepared and checked

Related questions

• 1 A person with a myopic eye can see clearly up to a distance of 1.2 m. What is the nature and power of the lens required to correct this defect of vision?
• 2 A hyperopic person can see distant objects clearly but cannot read a newspaper held at 25 cm without glasses. The far point of his eye is at infinity. Calculate the minimum power (in dioptres) of a thin converging lens that should be placed close to the eye to enable him to read at 25 cm.
• 3 Which part of the eye contributes the greatest refractive power?
• 4 Describe what happens to the ciliary muscle, suspensory ligaments and the shape of the lens when the eye focuses on a near object.
• 5 Which of the following statements correctly describes the changes that occur in the eye during accommodation for a near object?
• 6 A monochromatic red light (λ = 600 nm) and violet light (λ = 400 nm) pass through a prism whose apex angle is 30°. The refractive index of the prism for red light is 1.50 and for violet light is 1.55. Assuming small angles, calculate the angular dispersion between the red and violet rays after emerging from the prism.