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A divergent lens of focal length 30 cm forms the image of an object of size 6 cm on the same side as the object at a distance of 15 cm from its optical centre. - Science

A divergent lens of focal length 30 cm forms the image of an object of size 6 cm on the same side as the object at a distance of 15 cm from its optical centre. Use lens formula to determine the distance of the object from the lens and the size of the image formed.

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Solution

Given:

f = −20 cm (It is a diverging lens.)

v = −15 cm (Image is formed on the same side of the lens.)

Using the lens formula,

`1/f=1/v+1/u`

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

`=1/((-15))+1/((-30))=-1/30`

∴u = 30 cm

Given: Height of the object, h = 6 cm

Height of the image, h' = ?

Magnification,` m=v/u=(h')/h`

∴ `(h')=hv/u=6xx((-15))/((-30))`

∴ h' = 3 cm

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