Chapter 25, Problem 14P

To determine

How much longer is the nearsighted eye?

Answer to Problem 14P

Solution:

The length of the eye is $\text{0}\text{.27cm}$

Explanation of Solution

Given info:

The distance is $2.0\text{ cm}$ the image distance for an object at infinity (for normal eye). The focal length of the lens is also. $f=2.0\text{cm}$.

Object distance, $u=17\text{cm}$

Formula used:

Thin lens equation,

$\begin{array}{l}1/f=1/u+1/v\\ v=fu/u-f\end{array}$

Calculation:

Substituting the given values, in above equation we get,

$\begin{array}{l}v=fu/u-f\\ =2\times 17/17-2\\ =2.27\text{cm}\end{array}$

Therefore, the distance between the lens and the retina is

$\begin{array}{l}=2.27\text{cm}-\text{2cm}\\ \text{=0}\text{.27cm}\end{array}$