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Question

A converging lens of focal length 20 cm and a diverging mirror of focal length 10 cm are placed 5 cm apart with their principal axes coinciding. Where should an object be placed so that its image falls on itself?


A
50 cm
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B
100 cm
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C
50 cm
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D
100 cm
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Solution

The correct option is B 100 cm
Let the object be placed at a distance x from the pole of lens further away from the mirror.


From the figure,

u=x , f1=20 cm

Using lens formula,

1f=1v1u

Substituting the data we get,

120=1v1x

v=20xx20 .....(1)

For the ray to retrace its path, it should be incident normally on the convex mirror, or in other wrods the rays should pass through the center of curvature of mirror.

v=+5+2×10=+25 cm

Substituting this in (1) we get,

+25=20xx20

25x500=20x

x=100 cm

Hence , option (b) is the correct answer.

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