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

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

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Answer 1 · 2016-11-12T15:06:35

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