A lens of focal length 15cm forms an erect image three the size of the object .what is the distance between the object and image
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ANSWER
In△PAQ
Sumoftwooppositeinteriorangles=Exteriorangle
α=θ+∠θ−(i)
In△PAR
α+θ+∠R=180
∘
α=180
∘
−θ−∠R−(ii)
In△PMQ
∠MPQ=180−∠Q−90
∘
=90−∠Q
∠APM=∠APQ−∠MPQ
=θ−(90−∠Q)
=θ+∠Q−90
∘
−(iii)
∵(i)=(ii)
=>θ+∠Q=180−θ−∠R
=>2θ=180−∠Q−∠R
=>θ=90−
2
1
(∠Q+∠R)
puttingthisvalueofθin(iii)
∠APM=∠Q+90−
2
1
(∠Q+∠R)−90
=
2
∠Q
−
2
∠R
=
2
1
(∠Q−∠R)
∴a=2
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