Question

The image obtained with a convex lens is erect and its length is four times the length of the object. If the focal length of the lens is $20 \, cm$ , the object and image distances are

• A. $u=60 \, cm$ , $v=15 \, cm$
• B. $u=20cm$ , $v=10cm$
• C. $u=10cm$ , $v=20cm$
• D. $u=15cm$ , $v=60cm$

Answer 1

Answer: (D)

$f=20cm$ , $m=4$
$\therefore m=\frac{v}{u}=4\Rightarrow v=4u$
Using the formula, we have
$\frac{1}{f}=\frac{1}{v}-\frac{1}{u}$
$\frac{1}{20}=\frac{1}{u}-\frac{1}{u}\Rightarrow \frac{1}{20}=\frac{1 - 4}{4 u}$
$\Rightarrow \frac{1}{20}=\frac{- 3}{4 u}\Rightarrow 4u=-60$
$\therefore u=-15$
Putting the value of $u$ , we get
$v=4u=4\times \left(\right. - 15 \left.\right)=-60$
$\therefore $ Object distance $u=15cm$ , image distance $v=60cm$