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Question

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: (Assume paraxial ray approximation holds)

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 D 0.5m
His distance from the mirror is the
object distance, treating him as an object, So,
Applying mirror formula
1u+1v=1f
Here, u is negative and f for convex
mirror is positive , So,
1f+1v=1f
1v=2f
Also, m(magnification) =vu
m=⎢ ⎢ ⎢ ⎢2f(1f)⎥ ⎥ ⎥ ⎥1=12
We know,
m=imagelengthobjectlength
Here, object length = Boy's height = 1 m.
So,
m=imagelength1m=12
image length = 12=0.5m
Option - C is correct.

1112449_1114846_ans_0a603ab8cefc402f8b1320affb5a84fb.jpg

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