Question

A diverging lens has a focal length of 20cm, at what distance should an object of height 4cm from the optical centre of lens be placed so that it's image is formed 10cm away from the lens.Find the size of the image and draw the ray diagram to show the formation of the image

Answer 1

Answer:

Explanation:

Given :-

f = - 20 cm

h₁ = 4 cm

v = - 10 cm

To Find :-

u = ??

h₂ = ??

Solution :-

Using 1/f = 1/v - 1/u, we get

⇒ 1/u = - 1/10 + 1/20

⇒ 1/u = - 2 + 1/20

⇒ 1/u = - 1/20

⇒ u = - 20 cm

h₂ = (v/u)  h₁

⇒ h₂ = - 10/- 20 × 4

⇒ h₂ = 2 cm

2nd Part Diagram is provided in attachment.

Answer 2

Answer:

Size of the image is 2cm

Explanation:

Given focal length of a diverging lens, $f=-20cm$

height of object, $H=4cm$

image distance,  $v=-10cm$

Using the lens formula,

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

                                            $\implies \frac{1}{u}=\frac{-1}{10} - \frac{-1}{20}=-\frac{1}{20}$

                                            $\implies u = - 20 cm$

Therefore, the object distance is -20cm.

Using the relation of height of  object and image,

                $\frac{h}{H} =\frac{v}{u}\implies\ {h} =\frac{v}{u}\times H$

                                        $=\frac{-10}{-20}\times 4=2cm$

Therefore, the size of the image is 2cm