A thin convex lens of focal length $+12\text{cm}$ forms an image of a candle placed $30\text{cm}$ from the lens. Find (i) the image distance $v$, (ii) whether the image is real or virtual, (iii) whether it is upright or inverted, and (iv) the linear magnification $m$.

Step-by-step solution

1. Use the lens formula $\frac{1}{v}=\frac{1}{f}-\frac{1}{u}$ with $f=+12\text{cm}$ and $u=-30\text{cm}$ (object distance is taken negative for a real object).
2. Substitute: $\frac{1}{v}=\frac{1}{12}-\frac{1}{-30}=\frac{1}{12}+\frac{1}{30}=\frac{5+2}{60}=\frac{7}{60}$.
3. Hence $v=\frac{60}{7}\approx 8.57\text{cm}$? Wait sign error. Actually correct calculation: $\frac{1}{12}=0.0833$, $-\frac{1}{30}=-0.0333$, so $\frac{1}{v}=0.0833-0.0333=0.0500$, giving $v=20\text{cm}$ positive, meaning the image is on the opposite side of the lens (real).
4. Since $v$ is positive, the image is real and formed on the far side of the lens.
5. Magnification $m=\frac{v}{u}=\frac{+20}{-30}=-\frac{2}{3}$; the negative sign indicates the image is inverted relative to the object.

Concept tested: Lens formula and magnification

Published 14 September 2026 · How this solution was prepared and checked