CBSE Class 10 Science 2019 · Paper 31/3/3 · Question 18

(a) The image is (1) virtual, (2) erect, (3) diminished - one-third the size of the object - and (4) formed on the same side of the lens as the object, between the optical centre and the focus, $13.3$ cm from the lens ($\frac{1}{v}=-\frac{1}{20}-\frac{1}{40}$ gives $v=-13.3$ cm and $m=+\frac{1}{3}$). (b) A diminished image formed by a convex lens is real and inverted, so $m=\frac{v}{u}=-\frac{1}{3}$. With $u=-x$ and $v=\frac{x}{3}$, the lens formula gives $\frac{3}{x}+\frac{1}{x}=\frac{1}{20}$, so $x=80$ cm. The object is $80$ cm from the optical centre ($u=-80$ cm; the image forms at $v=+26.7$ cm).