A boy of height 1m 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
0.25m
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B
0.33m
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C
0.5m
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D
0.67m
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Solution
The correct option is C0.5m Let f be the focal length of a convex mirror. According to new cartesian sign convention, Object distance u = -f, focal length = +f Using mirror formula, 1u+1v=1f 1−f+1v=1for1v=1f+1f=2forv=f2 The image is formed at a distance f2 behind the mirror. Magnification m = −vu=−f/2−f=12
As magnification is positive so It is a virtual image. Also, m = Heightofimage(hI)Heightofobject(h0) ∴hI=mhO=12(1m)=0.5m