Question

An object 60cm tall is placed at on the principle axis of a convex and its 30cm tall image is formed on the screen placed at a distance of 40cm from the object . What is the focal length of the lens

Answer 1

Height of object = 70

Answer 2

Answer: The focal length of the lens is 26.67 cm.

Explanation:

Given that,

Height of the object h = 60 cm

Height of image h' = 30 cm

Distance of the object v = 40 cm

The magnification is

$m = -\dfrac{v}{u}$

$m =- \dfrac{v}{u}=\dfrac{30}{60}$

$-\dfrac{40}{u}=\dfrac{1}{2}$

$u = -80\ cm$

Using lens's formula

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

$\dfrac{1}{f}= \dfrac{1}{40}+\dfrac{1}{80}$

$\dfrac{1}{f}= \dfrac{3}{80}$

$f = \dfrac{80}{3}$

$f = 26.67\ cm$

Hence, The focal length of the lens is 26.67 cm.