Answer to Question #118773 in Optics for Jess

Question

A person with hypermetropia has a near point of 56 cm. This person wears glasses to correct their vision that have an optical power of +2.7 D.

If this person wears their glasses such that they sit 1.6 cm from their eye, how far away from the glasses is the closest object they can clearly see when wearing their glasses? (to 2 s.f and in cm)

Answer 1

A person with hyperopia has (near point) NP > 25 cm, and hence is unable to bring an object 25 cm away into sharp focus. A corrective lens can be used to correct hyperopia by imaging an object at distance D = 25 cm onto a virtual image at the patient's near point. From the thin lens formula, the required lens will have optical power P given by

$P=\frac{1}{D}-\frac{1}{NP}$

The calculation can be further improved by taking into account the distance between the spectacle lens and the human eye

$P=\frac{1}{D-0.016}-\frac{1}{NP-0.016}$

In our case

$2.7=\frac{1}{D-0.016}-\frac{1}{0.56-0.016}\to D=0.236 m$

https://courses.lumenlearning.com/physics/chapter/26-2-vision-correction/