At what distance from a concave lens of focal length 20 cm, should a 6 cm tall object be placed so that it forms an image at 15 cm from the lens ? Also determine the size of the image formed.

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#### Solution

Focal length of concave lens,* f *= −20 cm

Image distance, *v* = −15 cm (Negative sign is taken because of sign convention.)

Using the lens formula, we get:

`1/f=1/v-1/u`

`rArr1/(-20)=1/(-15)-1/u`

`rArr1/u=1/(-15)+1/20`

`rArr1/u=(-4+3)/60`

`rArru=-60" cm"`

The distance of the object from the mirror is 60 cm.

`h_i`is the size of the image formed.

`h_o`m=vu=hiho

We know that the image formed by the concave lens is virtual and erect.

The magnification is given as:

`m=v/u=h_i/h_o`

`(-15)/(-60)=h_i/6`

`rArrh_i=1.5" cm"`

Hence, the size of the image is 1.5 cm.

Concept: Magnification Due to Spherical Lenses

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