A U− shaped wire abcd of length 30cm is placed before a concave mirror having radius of curvature 20cm. Find the total length of the image of wire.
A
11cm
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B
10cm
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C
12cm
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D
14cm
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Solution
The correct option is B10cm For side ab, ho=+10cm u=−40cm f=−202=−10cm
So, m=ff−u ⇒m=−10−10−(−40)=−13 ⇒hiho=∣∣∣−13∣∣∣ ⇒hi10=13 ⇒hi=103cm .........(1)
Similarly, for side cd, hi=5cm .........(2)
For side bc,
End b, u=−40cm f=−10cm
So, 1v+1u=1f ⇒1v−140=−110 ⇒1v=−340 ⇒v=−403cm
End c, u=−30cm f=−10cm
So, 1v+1u=1f ⇒1v−130=−110 ⇒1v=−115 ⇒v=−15cm
So, length of image of bc=|−15|−∣∣∣−403∣∣∣=53cm .........(3)
From (1), (2) and (3)
Total length of the image of wire abcd=103+5+53=10cm
Why this question ?In order to avoid mistakes, divide the whole object in segmentsand then apply mirror formula and magnification formula forboundary segments.