Question

A man wearing glasses of power $+2D$, can read clearly a book placed at a distance of $40cm$, from the eye. The power of the lens required, so that he can read at $25cm$ from the eye is ?

• A. $+4.5D$
• B. $+4.0D$
• C. $+3.5D$
• D. $+3.0D$

Answer 1

The correct option is C $+3.5D$

$P=2$
$\Rightarrow f=\frac{1}{P}=\frac{1}{2}m=50cm$

$u=-40cm$

$\Rightarrow \frac{1}{f}=\frac{1}{v}-\frac{1}{u}$
$\Rightarrow \frac{1}{50}=\frac{1}{v}-\frac{1}{-40}$

$\Rightarrow \frac{1}{50}-\frac{1}{40}=\frac{1}{v}$

$\Rightarrow v=-200cm$

Now for new lens object distance = new near point =-$25cm$

$u_2=-25cm$

$v_2=-200cm$
$\Rightarrow \frac{1}{f}=\frac{1}{v_2}-\frac{1}{u_2}$

$=\frac{1}{-200}-\frac{1}{-25}$

$\frac{1}{f}=\frac{1}{25}-\frac{1}{200}=\frac{7}{200}c{m}^{-1}=\frac{7}{2}{m}^{-1}$

$P=\frac{1}{f}$ = $+3.5D$