A thin convex lens has a focal length of $12,\text{cm}$ and an object is placed $20,\text{cm}$ in front of it. Find the image distance (in cm) and state whether the image is real or virtual.

Step-by-step solution

1. Use the thin lens formula $\frac{1}{f}=\frac{1}{u}+\frac{1}{v}$.
2. Substitute $f=+12\text{cm}$ and $u=-20\text{cm}$ (object distance is taken negative for real object).
3. $\frac{1}{12}=\frac{1}{-20}+\frac{1}{v}\Rightarrow \frac{1}{v}=\frac{1}{12}+\frac{1}{20}=\frac{1}{7.5}$.
4. Invert to get $v=+7.5\text{cm}$? Wait calculation check: $\frac{1}{12}=0.0833$, $\frac{1}{-20}=-0.05$, so $\frac{1}{v}=0.0833-(-0.05)=0.1333$, hence $v=7.5\text{cm}$.
5. But sign convention: $v$ positive means image on same side as outgoing light; for convex lens a positive $v$ denotes real image behind lens.
6. Thus $v=+7.5\text{cm}$, image is real and inverted.

Concept tested: Thin lens formula and sign convention

Published 19 September 2026 · How this solution was prepared and checked