An object is placed at $u=-15\text{ cm}$ from a convex lens of focal length $f=+10\text{ cm}$. Where is the image $v$ formed?

Solution

1. Identify the given values: object distance $u=-15\text{ cm}$ and focal length $f=+10\text{ cm}$.
2. Apply the lens formula: $\frac{1}{v}-\frac{1}{u}=\frac{1}{f}$, which becomes $\frac{1}{v}-\frac{1}{-15}=\frac{1}{10}$.
3. Rearrange the equation to solve for $v$: $\frac{1}{v}=\frac{1}{10}-\frac{1}{15}$.
4. Calculate the common denominator: $$\begin{array}{rl}\frac{1}{v}& =\frac{3-2}{30}\\ & =\frac{1}{30}\end{array}$$, resulting in $v=30\text{ cm}$.
5. Hence the answer is (A).