Question

A person struggles to read by holding a book at arm's length, a distance of 49 cm away.

What power of reading glasses should be prescribed for her, assuming they will be placed 2.1 cm from the eye and she wants to read at the "normal" near point of 25 cm ?

Answer 1

first we have to define power as :

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

where P is power and f is the focus

$p=\frac{1}{f}=\frac{1}{a}+\frac{1}{b}$

where a is the distance from the point of view of the lens to the vertex b is the distance from the vertex to the image

now

a =2.1 and b=25 them

$p=\frac{1}{f}=\frac{1}{2.1}+\frac{1}{25}=0.5161\, \, \frac{1}{cm}$

but $p=51.61\, \, \frac{1}{m}$              we know that 1 diopters is the reciprocal of the focal length in meters

$p=51.61\, \, \frac{1}{m}= 0.019 \, \, diopters$