Question

A person is unable to see objects nearer than $50cm$. He wants to read a book placed at a distance of $25cm$. Find the nature of focal length and power of the lens, he needs for his spectacles.

Answer 1

Step 1: Find the focal length of the lens

Given,

$$\begin{gathered} u=-50cm \\ v=-25cm \end{gathered}$$

By lens formula,

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

Putting the values

$$\begin{gathered} \Rightarrow \frac{1}{f}=\frac{1}{-50}-\frac{1}{-25} \\ \Rightarrow \frac{1}{f}=\frac{1}{50} \\ \Rightarrow f=50cm \end{gathered}$$

Step 2: Find the power of the lenses

$Power=\frac{1}{focallength(inm)}$

Now,

$\Rightarrow P=\frac{100}{50}=+2D$

Hence, the power of the lens is $+2D$.