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Question

A point object is placed at a distance of 10 cm and its real image is formed at a distance of 20 cm from a concave mirror. If the object is moved by 0.1 cm towards the mirror the image will shift by (nearly)

A
0.4 cm away from the mirror
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B
0.8 cm away from the mirror
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C
0.4 cm towards the mirror
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D
0.8 cm towards the mirror
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Solution

The correct option is A 0.4 cm away from the mirror
From the relation,
1v+1u=1f
By differentiation mirror formula we have,
dvv2duu2=0
dv=v2u2(du)
From given data,
dv=(2010)2(0.1)=0.4 cm

As the change in the final distance is positive so the image will shift away from the mirror.
Why this question?

Caution: We can use differential formula only for small changes in object position

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