Question

An upright image which reduced in size 10 times occurred in a mirror. If the radius of

curvature of the mirror is 2 m, bow far is the object from the mirror?​

Answer 1

-10/9 m

Step-by-step explanation:

Radius of curvature, R=2 m

Focal length of mirror, f=R/2=2/2=1 m

Let height of object=h

Height of image, h'=h-10h=-9h

We have to find the distance of object from the mirror.

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

`m=(-9h)/(h)=-9`

Image is upright and small in size it means the mirror is convex.

Focal length of convex mirror is negative.

f=-1m

`-9=-(v)/(u)`

`v=9u`

Now, mirror formula

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

`(1)/(9u)+(1)/(u)=(1)/(1)`

`(1+9)/(9u)=-1`

`10=-9u`

`u=-(10)/(9) m`

Hence, the distance of object from the mirror is -10/9 m