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Question

A 5cm long needle lies along the principal axis axis of a concave mirror of focal length 20cm in such a way that the end closer to the pole is 40cm from it. Find the length of the image of the needle formed by the mirror.

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Solution

Given,

Length of needle, l=5cm

Focal length, f=20cm

(i) distance of near end of needle from pole of th emirror, u1=40cm
(ii) distance of far end of needle from pole of the needle from pole of the mirror, μ2=40+5

=45cm

for (i) , th eobject is at 2f, so its image will be at 2f

v1=2f=2×20=40cm

for (ii),

1f=1v21u2

120=145120

v2=36cm

length of the needle's image, l=|v2v1|=|4036|

l=4cm

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