Question

An object 2 cm tall is placed on the axis of a convex lens of focal length 5 cm at a distance of 10 cm from the optical centre of the lens. Find the nature, position and size of the image formed. Which case of image formation by convex lenses is illustrated by this example ?

Answer 1

Here, $h_o=2cm$

$f=5cm$

$u=-10cm$

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

$\Rightarrow \frac{1}{v}-\frac{1}{-10}=\frac{1}{5}$

$\Rightarrow \frac{1}{v}=\frac{1}{5}-\frac{1}{10}=\frac{1}{10}$

$\Rightarrow v=10cm$

So, the image is formed at a distance 10 cm on the other side of the object.

Now, $m=\frac{v}{u}=\frac{10}{-10}=-1$

So, the image formed is real, inverted and same size as the object. This is the case when object is placed at twice the focal length (2f).