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  4. A convex mirror forms an image one-fourth the size of the object. If the object is at a distance of 0.5 m from the mirror, the focal length of the mirror is

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Q. A convex mirror forms an image one-fourth the size of the object. If the object is at a distance of $0.5 \, m$ from the mirror, the focal length of the mirror is

NTA AbhyasNTA Abhyas 2020Ray Optics and Optical Instruments

Solution:

$\frac{f}{f - u}=\frac{1}{4}=\frac{f}{f - \left(\right. - 0.5 \left.\right)}$
Or $4f=f+0.5 \, or \, 3f=0.5$
Or $f=\frac{0.5}{3}m=0.17m$