Answer to Question #173123 in Optics for Jo Grayson

Question

A particular patient's eyes are unable to focus on objects closer than 36.5 cm and corrected lenses are to be prescribed so that the patient can focus on objects 21.0 cm from their eyes. If contact lenses are to be prescribed, determine the required lens power (in diopters).If eyeglasses are to be prescribed instead and the distance between the eyes and the lenses is 1.90 cm, determine the power (in diopters) of the required corrective lenses.

Answer 1

Given,

Object distance $(u)= 21cm$

Image distance $(v)=-36.5cm$

$\frac{1}{f}=\frac{1}{v}-\frac{1}{u}$

Now, substituting the values,

$\Rightarrow \frac{1}{f}=\frac{1}{21}+\frac{1}{36.5}$$=\frac{57.5}{766.5}$

$\Rightarrow$ $P=\frac{100\times 57.5}{766.5}=7.5D$

If the distance between the eye and the lens be 1.9cm then new image distance $(v_n)=-(36.5-1.9)cm$

$=-34.6cm$

$u=21-1.9=19.1cm$

Now, substituting the values in the lens equation,

$\frac{1}{f}=\frac{1}{v}-\frac{1}{u}$

$=\frac{1}{34.6}+\frac{1}{19.1}=\frac{34.6+19.1}{19.1\times 34.6}$

$\frac{1}{f}=\frac{15.5}{660.86}$

$P=\frac{1550}{660.86}=2.34D$