A concave mirror has a focal length of $f=-20\text{ cm}$. If an object is placed at a distance of $u=-30\text{ cm}$ from the mirror, what is the image distance $v$?

Solution

1. Identify the given values: focal length $f=-20\text{ cm}$ and object distance $u=-30\text{ cm}$.
2. Apply the mirror formula: $\frac{1}{v}+\frac{1}{u}=\frac{1}{f}$.
3. Substitute the values into the equation: $\frac{1}{v}+\frac{1}{-30}=\frac{1}{-20}$.
4. Rearrange to solve for $v$: $$\begin{array}{rl}\frac{1}{v}& =\frac{1}{-20}+\frac{1}{30}\\ & =\frac{-3+2}{60}\\ & =-\frac{1}{60}\end{array}$$.
5. Calculate the final result: $v=-60\text{ cm}$.
6. Hence the answer is (A).