Question

A tree has a height of 3.40 cm and is placed in front of a concave mirror. The image of the tree is inverted, 1.60 cm tall, and located 14.0 cm in front of the mirror. Find the focal length of the mirror.

Answer 1

9.52 cm

Step-by-step explanation:

Height of tree that is height of object O =3.40 cm

Height of image that is I =1.60 cm

We know that magnification
`m=(hieght\ of\ image)/(height\ of\ object)=(-1.60)/(3.40)=-0.47` negative sign for the inverted image

We also know that
`m=(-v)/(u)`

`-0.47=(-14)/(u)`

u=29.78 cm

Now for concave mirror
`(1)/(f)=(1)/(u)+(1)/(v)`

`(1)/(f)=(1)/(14)+(1)/(29.78)`

`(1)/(f)=0.105`

f=9.52 cm