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Question

An object is placed in front of a convex mirror at 60 m from the mirror. Its radius of curvature is 40 m. The object starts moving towards the mirror at 20 m s1. Find the average speed of the image after a time interval of 2 seconds?

A
10 m s1
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B
20 m s1
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C
2.5 m s1
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D
5 m s1
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Solution

The correct option is B 2.5 m s1
Given:
The distance of object u from the pole is 60 m,
Radius of curvature (r)=40 m
Let f be the focal length and v be the image distance
We know that,
f=r2=12×40=20 m.
Applying the sign conventions, u=60 m and f=+20 m
We know, 1v + 1u = 1f
1v - 160 = 120
v=15 m
Positive sign shows that the image is virtual. Speed of the object =20 ms1 and time taken =2 s
Distance = Speed × time
20×2=40 m
Therefore, now the position of object will be u=6040=20 m
Let v be the new position of the image
Applying it in the mirror formula we get,
1v + 1u = 1f
1v - 120 = 120
1v = 4020×20
v=10 m
So, the image moves from 15 m to 10 m in 2 s. Hence, its average speed = 15102=2.5 m s1

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