Question

An object 4 cm high is placed at a distance of 10 cm from a convex lens of focal length 20 cm. Find the position, nature and size of the image.

Answer 1

Here, $u=-10cm$

$f=20cm$ and $h_o=4cm$

From the lens formula, $\frac{1}{v}-\frac{1}{u}=\frac{1}{f}$

$\Rightarrow \frac{1}{v}-\frac{1}{-10}=\frac{1}{20}$

$\Rightarrow \frac{1}{v}=\frac{1}{20}-\frac{1}{10}=\frac{-1}{20}$

$\Rightarrow v=-20cm$

Hence, the image is formed at a distance 20 cm on the same side as the object.

Now, $m=\frac{v}{u}=\frac{-20}{-10}=2$

$\Rightarrow \frac{h_i}{h_o}=2$

$\Rightarrow \frac{h_i}{4}=2$

$\Rightarrow h_i=8cm$

Hence, the image is virtual, erect and magnified.