Question

An erect image 2.0 cm high is formed 12 cm from a lens, the object being 0.5 cm high. Find the focal length of the lens.

Answer 1

Step 1, Given data

Image distance, $v=-12cm$,

Height of the image, $h_i=2cm$

Height of the object, $h_o=0.5cm$

Step 2, Finding the focal length

Since the size of the image is greater than that of the object and a virtual image is being formed, the lens is convex in nature.

We know,

Magnification, $m=\frac{h_i}{h_o}=\frac{v}{u}$

Putting all the values

$\Rightarrow \frac{2}{0.5}=\frac{v}{u}$

$\Rightarrow u=\frac{v}{4}=-3cm$

Therefore the object distance is 3 cm

Now,

Using the lens formula,

$\frac{1}{v}-\frac{1}{u}=\frac{1}{f}$

Putting all the values

$\frac{-1}{12}+\frac{1}{3}=\frac{1}{f}$

After solving

f = 4 cm

Hence the focal length of the lens is 4 cm