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Question

# A convex mirror of focal length 20 cm is fitted to a motor car. If the second car with width 2 m and height 1.6 m is 6 m behind the first car and overtakes the first car at a relative speed of 15 m/s, then how fast will the image of the second car in the convex mirror of first car be moving?

A
0.016 m/s
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B
0.026 m/s
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C
0.036 m/s
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D
0.046 m/s
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Solution

## The correct option is A 0.016 m/sFor the given convex mirror of first car the second car is 6 m behind, u=−6 m=−600 cm f=+20 cm Using mirror formula, 1v+1u=1f 1v−1600=120 ⇒1v=31600 or, v=60031 cm Using the relation for magnification produced by mirror, m=−vu=(−60031)−600=131 Also, velocity of the image when the object is moving along the principal axis is given by, vi=−m2vo Here v0=15 m/s is the relative velocity of object w.r.t mirror. ⇒vi=−(131)2×15≃−0.016 m/s Hence, the speed of the image will be 0.016 m/s. Why this question ?Caution: Dimension of object is given to confuse the students.Tips: Remember that we consider only point object in the formula of image velocity and ignore the dimensions.

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