Question

An object is placed 11.0 cm in front of a concave mirror whose focal length is 24.0 cm. The object is 2.60 cm tall. What is the height of the image? (cm)

Answer 1

Answer:

Height of the image is 4.79 cm.

Explanation:

Object distance, u = -11 cm

Focal length of the mirror, f = -24 cm

Height of the object, h = 2.6 cm

We need to find the height of the image. Firstly, using the mirror's formula as :

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

v is the image distance

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

$\dfrac{1}{v}=\dfrac{1}{(-24)}-\dfrac{1}{(-11)}$

v = 20.30 cm

The magnification of the image is given by :

$m=\dfrac{-v}{u}=\dfrac{h'}{h}$, h' is the height of the image

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

$\dfrac{-20.30}{-11}\times 2.6={h'}$

h' = 4.79 cm

So, the height of the image is 4.79 cm. Hence, this is the required solution.