Question

A person needs a lens of power $-5.5$ dioptres for correcting his distance vision. For correcting his near vision he needs a lens of power $+1.5$ dioptre. What is the focal length of the lens required for correcting (i) distance vision, and (ii) near vision?

Answer 1

(i) Distant Vision :

Given,

Power $=5.5D$

Power, $P=\frac{1}{f}$

Focal length, $f=\frac{1}{P}$

$\Rightarrow f=\frac{1}{-5.5}$

$\Rightarrow f=\frac{10}{-55}$

$\Rightarrow f=\frac{2}{-11}$

$\Rightarrow f=-0.181m$

$\Rightarrow f=-18.1cm$

(ii) Near Vision :

Given,

Power $=1.5D$

$P=\frac{1}{f}$

$f=\frac{1}{P}$

$\Rightarrow f=\frac{1}{1.5}$

$\Rightarrow f=\frac{10}{15}$

$\Rightarrow f=\frac{2}{3}$

$\Rightarrow f=0.667m$

$\Rightarrow f=66.7cm$