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Question

A point object is moving with speed V0 towards a concave mirror with radius of curvature R, along the principal axis. The speed of the image is not defined when the object is :

A
at focus
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B
at pole
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C
in the middle of line joining focus and centre of curvature
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D
at centre of curvature
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Solution

The correct option is A at focus
We know from mirror formula that,
1v+1u=1f=2R
Using sign convention for concave mirror :
1v+1u=1f=2R

1v=2R1u

1v=2u+RRu

v=RuR2u

And magnification (m) is given by
m=vu
m=RuR2uu=RR2u

For motion of the object along the principal axis,
velocity of image, Vi=m2Vo

Vi=(RR2u)2Vo .........(1)

Eq.(1) is not defined when R2u=0
u=R2 [at focus]

Hence, when the object is at focus, the speed of the image is not defined.


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