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

Options

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

Answer

b.

Explanation

In first case, if object distance is x, mage 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, `(1)/(f)=-(5)/(x)`
In second case, `(1)/(f)=-(3)/((x-5))`
Solving we get, `x=12.5cm` and `f=2.5cm` and hence `|f|=2.5cm`