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

Height of the image is 4.79 cm.

Step-by-step 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 :

`(1)/(f)=(1)/(v)+(1)/(u)`

v is the image distance

`(1)/(v)=(1)/(f)-(1)/(u)`

`(1)/(v)=(1)/((-24))-(1)/((-11))`

v = 20.30 cm

The magnification of the image is given by :

`m=(-v)/(u)=(h')/(h)`, h' is the height of the image

`(-v)/(u)* h={h'}`

`(-20.30)/(-11)* 2.6={h'}`

h' = 4.79 cm

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