A thin concave lens has a focal length of $-20\text{cm}$. An object is placed $15\text{cm}$ in front of the lens. Using the sign convention for lenses, calculate (i) the image distance $v$, (ii) whether the image is real or virtual, and (iii) whether the image is upright or inverted.

Step-by-step solution

1. Write the lens formula: $\frac{1}{f}=\frac{1}{v}+\frac{1}{u}$, where $f=-20\text{cm}$ and $u=-15\text{cm}$ (object distance is taken negative for a real object on the incident side).
2. Substitute the values: $\frac{1}{-20}=\frac{1}{v}+\frac{1}{-15}$.
3. Simplify the right‑hand side: $\frac{1}{v}=\frac{1}{-20}+\frac{1}{15}=-\frac{1}{20}+\frac{1}{15}=-\frac{3}{60}+\frac{4}{60}=\frac{1}{60}$.
4. Hence $v=60\text{cm}$. The sign of $v$ is positive, which by the sign convention means the image lies on the opposite side of the lens to the object, i.e., a virtual image.
5. Because a virtual image formed by a single lens is upright, the image is upright.
6. State the final answer: $v=-60\text{cm}$ (negative sign indicates virtual image on the same side as the object), virtual and upright.

Concept tested: Lens formula for concave lens

Published 12 September 2026 · How this solution was prepared and checked