Chapter 25, Problem 18P

To determine

The near and far points of the contact lens.

Answer to Problem 18P

Solution:

Near point is 18.41cm and far point is 1m.

Explanation of Solution

Given:

$P=-\text{4D}$

Formula used:

$\begin{array}{l}\frac{1}{f}=\frac{1}{u}+\frac{1}{v}\\ P=\frac{1}{f}\end{array}$

Calculation:

According to lens equation,

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

For near point image distance is considered as 10.6cm.

Thus, $\frac{1}{f}=\frac{1}{u}+\frac{1}{v}$

$\begin{array}{l}P=\frac{1}{u}+\frac{1}{v}\\ P-\frac{1}{v}=\frac{1}{u}\\ -4-\frac{1}{-0.106}=\frac{1}{u}\\ u=18.41\text{cm}\end{array}$

For near point image distance is considered as 20cm.

Thus, $\frac{1}{f}=\frac{1}{u}+\frac{1}{v}$

$\begin{array}{l}P=\frac{1}{u}+\frac{1}{v}\\ P-\frac{1}{v}=\frac{1}{u}\\ -4-\frac{1}{-0.20}=\frac{1}{u}\\ u=1\text{m}\end{array}$