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Given image distance v = 24 cm
magnification = - 1
Also we know magnification m = -v/u ; where u = object distance
Thus u= (-24)/-1 =24 cm.
Again from lens maker formula we have,
(1/v)+(1/u)=(1/f) ; here f = focal length of the lens.
(1/f) = (1/24)+(1/24) = (2/24)
f = 12 cm
Now when the object is displaced by a distance of 18 cm towards the lens, the new object distance will u₁ =24 -18 = 6 cm
Now solving for image distance v₁
(1/v₁)+(1/u₁)=(1/f)
(1/f) - (1/u₁) = (1/v₁)
(1/v₁) = (1/-12) - (1/6)
v₁ = - 4 cm.
The image will be formed behind the lens and will be real and inverted.
Note - Not mentioned whether the image is formed behind or in front of the lens.
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