A convex lens forms an image at the distance $40cm$ on other side of the lens when an object which is placed at $40cm$ away from it . The object is then moved $10cm$ towards the lens then, where will be the image shift?

The correct option is D $20cm$ away from lens.
Initially,
Object distance from the lens, $u=-40cm$
Image distance from the lens, $v=40cm$

Image distance is equal to the object distance. This happens when object is at $2f$ distance from the lens.
$2f=40$
$f=20cm$

When the object is moved $10cm$ towards the lens, new object distance is:
$u^{\prime }=-(40-10)cm$
$u^{\prime }=-30cm$

Applying lens formula, the new image distance $v^{\prime }$ is
$\frac{1}{20}=\frac{1}{v^{\prime }}-\frac{1}{(-30)}$
$v^{\prime }=60cm$

Shift in image is:
$\Delta v=v^{\prime }-v$
$\Delta v=60-40=20cm$
Thus, the image shift is $20cm$ away from the convex lens.