Question

An object that is 2 cm tall is 18 cm in front of a converging lens and creates a real image 8 cm beyond the lens. What is the focal length of the lens?
What is the height of the image?

Answer 1

Answer:

The focal length of the lens is 5.54 cm and the height of the image is -0.89 cm.

Explanation:

Given that,

Height of object h = 2 cm

Object distance u= -18 cm

Image distance v= 8 cm

We need to calculate the focal length of the lens

Using formula of lens

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

Where, f = focal length

Put the value into the formula

$\dfrac{1}{f}=\dfrac{1}{8}-\dfrac{1}{-18}$

$\dfrac{1}{f}=\dfrac{13}{72}$

$f=5.54\ cm$

(II). We need to calculate the height of the image

Using formula of magnification

$m =\dfrac{v}{u}=\dfrac{h'}{h}$

$\dfrac{v}{u}=\dfrac{h'}{h}$

Put the value into the formula

$\dfrac{8}{-18}=\dfrac{h'}{2}$

$h'=\dfrac{8}{-18}\times2$

$h'=-0.89\ cm$

Hence, The focal length of the lens is 5.54 cm and the height of the image is -0.89 cm.