A concave mirror of focal length 10cm. A square wire of side 3cm is placed 23cm away from the mirror. The centre of the square lies on the principal axis. What is the area enclosed by the image?

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Answer 1 · 2017-09-19T11:08:10

We know that conjugate foci relation of spherical mirror Is as follows

$1/v+1/u=1/f$ ,

Where

$v->"image distance"=?$

$u->"object distance"=-23cm$

$f->"focal length"=-10cm$

$1/v-1/23=-1/10$

$=>v=-230/13$ cm

Magnification $m=v/u=(230/13)/23=10/13$

Length of each side of the square frame is $3$ cm

If the plane of the square wire frame is kept vertical with the principal axis the length of each side of its image will be $3xx10/13=30/13$ cm

Hence area enclosed by the image will be $(30/13)^2cm^2~~5.33 cm^2$