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Q.

The height of a candle flame is 5 cm. A lens produces an image of this flame 15cm high on a screen. The candle is then moved over a distance 1.5 cm away from the lens and a sharp of the flame 10cm high is obtained after shifting the screen. Determine the focal length of the lens (in cm)
 

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answer is 9.

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Detailed Solution

For convex lens forming real image
 1v+1u=1f
m=155=vu   or  3u=v
 13u+1u=1f or  u=4f3 and  v=4f
In the second position  u'=u+15=4f3+1.5
 m'=v'u'=105
 v'=2u'=2(4f3+1.5)=8f3+3
 1v1+1u'=1f'
Or  1(8f3)+3+1(4f3)+1.5=1f
 f=9cm  or  1.125cm
Only  f=9cm is correct answer. The other value is absurd

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