Question

An object of height 5cm is placed at a distance 30 cm from the convex lens of focal length 10 cm. The height of image of the object is :
1: 2 cm
2: 2.5 cm
3: 1.5 cm
4: 5 cm

Choose the correct answer.​

Answer 1

Explanation:

Given : -

Height of object, h₁ = 5 cm

Position of object, u = - 30 cm

Focal length , f = 10 cm

Height of image , h₂ = ?

Using lens formula , we know that ,

$\frac{1}{f} = \frac{1}{v} - \frac{1}{u} \\ \\ \frac{1}{10} - \frac{1}{v} - \frac{1}{ - 30} \\ \\ \frac{1}{v} = \frac{1}{10} - \frac{1}{30} \\ \\ \frac{1}{v} = \frac{3 - 1}{30} \\ \\ \frac{1}{v} = \frac{2}{30} = \frac{1}{15} \\ \\ v \: = 15 \: cm$

Now ,

Using Magnification of lens , we know that ,

$\frac{v}{u} = \frac{h2}{h1} \\ \\ \frac{15}{ - 30} = \frac{h2}{5} \\ \\ h2 = \frac{5}{ - 2} = - 2.5 \\ \\ h2 = - 2.5 \: cm \:$

Therefore ,

Height of image of the object will be 2.5 cm .

(negative sign in h₂ = -2.5 cm shows that image formed is inverted)