Chapter 25, Problem 10P

A person struggles to read by holding a book at arm’s length, a distance of 52 cm away. What power of reading glasses should be prescribed for her, assuming they will be placed 2.0 cm from the eye and she wants to read at the “normal" near point of 25 cm?

To determine

The power of the reading glasses

Answer to Problem 10P

Solution:

The power of the reading glasses are $2.52\text{D}$.

Explanation of Solution

Given:

Distance the person wants to read, $D_i=-52\text{cm}$

Normal near point, $D=25\text{cm}$

Distance of glass from the eye, $d=2\text{cm}$

Formula used:

The power of the reading glasses is calculated as

$P=\frac{1}{d_o}+\frac{1}{d_i}$

Here,

$d_o$ is the distance of the object

$d_i$ is the distance of image

Calculation:

Distance the person wants to read, $D_i=-52\text{cm}$, here negative sign indicates that the image form in the opposite direction of the lens.

The distance of the object from the eyes is $d_i=25-2=23\text{cm}$

The power of the reading glasses is calculated as

$\begin{array}{c}P=\frac{1}{d_o}+\frac{1}{d_i}\\ =\frac{1}{0.23}-\frac{1}{0.56}\\ =2.52\text{D}\end{array}$