Question

# A boy of height 1 m stands in front of a convex mirror. His distance from the mirror is equal to its focal length. The height of his image is:

A
0.25 m
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B
0.33 m
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C
0.5 m
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D
0.67 m
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Solution

## The correct option is C 0.5 mLet f be the focal length of a convex mirror.According to new cartesian sign convention,Object distance u = -f, focal length = +fUsing mirror formula, 1u+1v=1f1−f+1v=1for1v=1f+1f=2forv=f2The image is formed at a distance f2 behind the mirror.Magnification m = −vu=−f/2−f=12As magnification is positive so It is a virtual image.Also, m = Heightofimage(hI)Heightofobject(h0)∴hI=mhO=12(1m)=0.5m

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