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A thin pencil of length 20 cm is kept along the principal axis of a concave mirror of curvature 30 cm. Nearest end of the pencil is 20 cm from the pole of the mirror. What will be the size of image of the pencil?

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For the pencil kept along the principal axis and the end of the pencil closest to pole is at 20 cm,

say, u1 = -20 cm

Flence, the other end of the stick is at distance, u2 = (u1 + 20) = -40 cm from pole of the mirror.

As R = -30 cm, F = \(\frac{R}{2}\) = -15 cm

Using mirror formula for concave mirror,

Also, for other end of the stick,

∴ v2 = -24 cm

Here, negative signs indicate that images are formed on the left of the mirror.

The length of the image formed is given by,

v = v2 – v1 = -24 – (-60) = 36 cm.

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