Question

The image produced by a concave mirror is one-quarter the size of object. If the object is moved $5cm$ closer to the mirror, the image will only be half the size of the object. The focal length of mirror is

• A. $f=5.0cm$
• B. $f=2.5cm$
• C. $f=7.5cm$
• D. $f=10cm$

Answer 1

The correct option is B $f=2.5cm$

In first case, if object distance is $x$, image distance $=x/4$.
While it is $2^{nd}$ case, object distance becomes $(x-5cm)$ and image distance $(x-5cm)/2$. Using mirror formula we get,
In first case, $=\frac{1}{f}=-\frac{5}{x}$
In second case, $\frac{1}{f}=-\frac{3}{(x-5)}$
Solving we get, $x=12.5cm$ and $f=-2.5cm$ and hence $|f|=2.5cm$.