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प्रश्न
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.
उत्तर
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.
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