Question

An object of length `2cm` is placed at a distance of `2.5*f` from a concave mirror where f is its focal length. what is the length of the IMAGE?

length is provided and not the hieght.just need the length of image. PLease as fast as possible.

Answer 1

The conjugate foci relation of spherical mirror is

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

Where

`v->"Image distance"=?`

`u->"Object distance"=-2.5f`

`f->"Focal length"=-f`

So inserting the values in equation (1)

`1/v-1/(2.5f)=-1/f`

`=>1/v-1/(2.5f)=-1/f`

`=>1/v=-1/f+1/(2.5f)`

`=>1/v=-1/f+2/(5f)=(-5+2)/(5f)=-3/(5f)`

`=>v=-(5f)/3`

Negative means real and inverted image

Now Magnification `m-=v/u=((5f)/3)/((5f)/2)=2/3`

So `"size of image"=mxx"size of object"=2/3xx2cm=4/3cm`