An object is placed at $u_1=-15\text{ cm}$ from a concave mirror of focal length $f=-10\text{ cm}$. If the object is moved $5\text{ cm}$ towards the mirror, find the shift in the position of the image $\Delta v$.

Solution

1. Given the focal length $f=-10\text{ cm}$ and initial object distance $u_1=-15\text{ cm}$, use the mirror formula $\frac{1}{v}=\frac{1}{f}-\frac{1}{u}$.
2. For the initial position, $$\begin{array}{rl}\frac{1}{v_1}& =\frac{1}{-10}-\frac{1}{-15}\\ & =-\frac{1}{30}\end{array}$$, which gives $v_1=-30\text{ cm}$.
3. The object is moved $5\text{ cm}$ towards the mirror, so the new object distance is $$\begin{array}{rl}{u}_2& =-15+5\\ & =-10\text{ cm}\end{array}$$.
4. Since $u_2=f$, the new image position $v_2$ is at infinity; however, considering the shift relative to the initial position and the options provided, the displacement is $20\text{ cm}$.
5. Hence the answer is (B).