When an object is placed at a distance of 50cm from a convex lens, an image of a same size as the object is formed. What will be the nature of the image formed when the object is at a distance of:
a) 20cm from the lens
b) 30cm from the lens

Since an image of equal size is formed when the object is placed at 50cm, we infer that radius of curvature of the convex lens is 50cm. Hence f = R/2 = 50/2 = 25cm.

a) Object is at 20cm
20cm < 25cm Hence the object is between the F1 and optic centre of the lens.
Hence image formed will be virtual, erect, extremely magnified, beyond C1 and on the same side as the object.

b) 30cm
​Here the object is between F1 and C1 (between 25cm and 50cm) of the lens.
Hence image formed will be real, inverted, beyond C2, magnified and on the other side of the lens.

Hope this helps! :)