Question

An object of the height of 2 cm is placed perpendicular to the principal axis of a concave lens of the focal length of 12 cm. find the height of the image, if the object is placed at a distance of 8 cm from the lens?

Answer 1

Step 1, Given data

Height of the object $H_o=2cm$

Focal length f = -12 cm (Concave lens)

Object distance u = -8 cm

Step 2, Finding the height of the image

From the lens formula

We know,

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

Putting all the values

$\frac{1}{v}+\frac{1}{8}=\frac{-1}{12}$

After solving

$v=\frac{-24}{5}$

Now we know,

Magnification = $m=\frac{v}{u}=\frac{H_i}{H_o}$

Putting all the values

$\frac{\frac{-24}{5}}{-8}=\frac{H_i}{2}$

After solving

$H_i=1.2cm$

Hence the height of the image formed will be 1.2 cm