Physics - Geometrical Optics Question with Solution | TestHub

Object is placed at distance $2f$ from the lens. So first image $I_1$ will be formed at distance $2f$ on other side. This image $I_1$ will behave like a virtual object for mirror. The second image $I_2$ will be formed at distance $20\mathrm{cm}$ in front of the mirror, or at distance $10\mathrm{cm}$ to the left hand side of the lens.
Now applying lens formula $$\begin{array}{rl}& \frac{1}{v}-\frac{1}{u}=\frac{1}{f}\\ & \frac{1}{v}-\frac{1}{+10}=\frac{1}{+15}\\ \text{ or }& v=6\mathrm{cm}\end{array}$$ Therefore, the final image is at distance $16\mathrm{cm}$ from the mirror. But, this image will be real. This is because ray of light is travelling from right to left. $\therefore$ The correct option is (b).