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Question

A U shaped wire abcd of length 30 cm is placed before a concave mirror having radius of curvature 20 cm. Find the total length of the image of wire.


A
11 cm
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B
10 cm
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C
12 cm
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D
14 cm
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Solution

The correct option is B 10 cm
For side ab,
ho=+10 cm
u=40 cm
f=202=10 cm
So, m=ffu
m=1010(40)=13
hiho=13
hi10=13
hi=103 cm .........(1)
Similarly, for side cd,
hi=5 cm .........(2)
For side bc,
End b,
u=40 cm
f=10 cm
So, 1v+1u=1f
1v140=110
1v=340
v=403 cm
End c,
u=30 cm
f=10 cm
So, 1v+1u=1f
1v130=110
1v=115
v=15 cm
So, length of image of bc =|15|403=53 cm .........(3)


From (1), (2) and (3)
Total length of the image of wire abcd =103+5+53=10 cm

Why this question ?In order to avoid mistakes, divide the whole object in segmentsand then apply mirror formula and magnification formula forboundary segments.

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