Question

An object with a height of 4.0 cm is placed 30.0 cm from a lens. The resulting inverted image has a height of 1.5 cm. What is the focal length of the lens? A. 15 cm B. 7.5 cm C 17 cm D. 8.2 cm E. 21 cm

Answer 1

Answer:

Focal length of the lens is 8.2 cm.

Explanation:

It is given that,

Height of object, h = 4 cm

Object distance, u = -30 cm

Height of the image, h' = -1.5 cm (negative because the image is inverted)

We need to find the focal length of the lens. It can be calculated using lens formula as :

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

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

$\dfrac{v}{-30}=\dfrac{-1.5}{4}$

Image distance, v = 11.25 cm

$\dfrac{1}{11.25}-\dfrac{1}{-30}=\dfrac{1}{f}$

f = 8.18 cm

or f = 8.2 cm

So, the focal length of the lens is 8.2 cm. Hence, this is the required solution.