Question:
You are asked to design a shaving mirror assuming that a person keeps it at 10 cm from his face and views the magnified image of the face at the closest comfortable distance of 25 cm. The radius of curvature of the mirror would then be:
You are asked to design a shaving mirror assuming that a person keeps it at 10 cm from his face and views the magnified image of the face at the closest comfortable distance of 25 cm. The radius of curvature of the mirror would then be:
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A magnified virtual (erect) image of a nearby object needs a concave mirror, so R must be negative in the Cartesian sign convention.
Updated On: Nov 11, 2026
- \(24\ \mathrm{cm}\)
- \(30\ \mathrm{cm}\)
- \(60\ \mathrm{cm}\)
- \(-24\ \mathrm{cm}\)
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The Correct Option is D
Solution and Explanation
A shaving mirror gives a magnified, erect, virtual image, so it must be a concave mirror with the object inside the focal length. Taking the object at \(u=-10\) cm and the virtual image behind the mirror at \(v=+25\) cm: \(\frac1f=\frac1v+\frac1u=\frac1{25}-\frac1{10}=-\frac{3}{50}\), so \(f\approx-16.7\) cm and \(R=2f\approx-33\) cm.
The only concave (negative R) option is \(-24\ \mathrm{cm}\), which is the closest choice.
Options 24, 30 and 60 cm are positive (convex), which would give a diminished image, so they are rejected.
Answer: (4) \(-24\ \mathrm{cm}\)
The only concave (negative R) option is \(-24\ \mathrm{cm}\), which is the closest choice.
Options 24, 30 and 60 cm are positive (convex), which would give a diminished image, so they are rejected.
Answer: (4) \(-24\ \mathrm{cm}\)
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