Question

Find the position and nature of the image of an object 5 cm high and 10 cm in front of a convex lens of focal length 6 cm.

Answer 1

Here, $u=-10cm$

$f=6cm$

and $h_o=5cm$

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

$\Rightarrow \frac{1}{v}-\frac{1}{-10}=\frac{1}{6}$

$\Rightarrow \frac{1}{v}=\frac{1}{6}-\frac{1}{10}=\frac{1}{15}$

$\Rightarrow v=15cm$

So, the image is formed at a distance of 15 cm on the other side of the object.

Now, $m=\frac{v}{u}=\frac{15}{-10}=-1.5$

$\Rightarrow \frac{h_i}{h_o}=\frac{h_i}{5}=-1.5$

$\Rightarrow h_i=-7.5cm$

Hence, the image is real, inverted and magnified.