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

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

Ray Optics and Optical Instruments

Solution:

$\frac{1}{4}=\frac{f}{x_{0}-f} $
$\frac{1}{2}=\frac{f}{x_{0}-5-f}$
Solving above two equations,
we get $f=2.5 \,cm$.