Question

A person has near point at $100\text{cm}$. What power of lens is needed to read at $20\text{cm}$ if the person uses spectacle, having glasses $2\text{cm}$ away from the eye?

• A. $4.54\text{D}$
• B. $3.54\text{D}$
• C. $5.00\text{D}$
• D. $5.54\text{D}$

Answer 1

The correct option is A $4.54\text{D}$

Given:

Near point, $D=100\text{cm}$

Since, the spectacle is placed $2\text{cm}$ away from the eye, so, the object distance will be $20\text{cm}-2\text{cm}=18\text{cm}$

$\therefore u=-18\text{cm}$

To be able to read, the image should form at near point of the eye.

Also, image distance will be $100\text{cm}-2\text{cm}=98\text{cm}$

$\therefore v=-98\text{cm}$

Now,

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

$\Rightarrow \frac{1}{f}=\frac{1}{(-98)}-\frac{1}{(-18)}$

$\therefore f=\frac{441}{20}\text{cm}=\frac{441}{2000}\text{m}$

So, power,

$P=\frac{1}{f}=\frac{1}{441/2000}=4.54\text{D}$