Question

An object is placed 10.0 cm in front of a concave mirror whose focal length is 23.0 cm. The object is 3.20 cm tall. What is the height of the image?

Answer 1

The height of the image is 2.23 cm.

Step-by-step explanation:

Given that,

Object distance = 10.0 cm

Focal length = -23.0 cm

Height of the object = 3.20 cm

We need to calculate the distance of image

Using image formula

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

`(1)/(v)=(1)/(-23.0)+(1)/(-10)`

`(1)/(v)=-(33)/(230)`

`v=-6.96\ cm`

We need to calculate the height of image

Using formula of magnification

`m = (-v)/(u)=-(h')/(h)`

`-(v)/(u)=-(h')/(h)`

Put the value into the formula

`(-6.96)/(-10)=(h')/(3.20)`

`h'=(-6.96*3.20)/(-10)`

`h'=2.23\ cm`

Hence, The height of the image is 2.23 cm.