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Question
An object of height 4 cm is placed at a distance of 15 cm in front of a concave lens of power, −10 dioptres. Find the size of the image.
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Solution
Object distance u = -15 cm
Height of object h = 4 cm
Power of the lens p = -10 dioptres
Height of image h' = ?
Image distance v = ?
Focal length of the lens f = ?
We know that:
`p=1/f`
`f=1/p`
⇒`f=1/-10`
⇒ `f=-0.1m =-10 cm`
From the lens formula, we have:
`1/v-1/u=1/f`
`1/v-1/-15=1/-10`
⇒`1/v+1/15=-1/10`
⇒`1/v=-1/15-1/10`
⇒`1/v=(-2-3)/30`
⇒`1/v=-5/30`
⇒`1/v=-1/6`
⇒`v=-6` cm
Thus, the image will be formed at a distance of 6 cm and in front of the mirror.
Now, magnification m =`v/u=(h')/h`
or `(-6)/(-15)=(h')/4`
`h'=(6x4)/15`
`h'=24/15`
∴`h'=1.6 cm`
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