Question

Two thin convex lenses of focal lengths f1 and f2 are separated by a horizontal distance d (where d>f1,d>f2), and their centre are displaced by a vertical separation Δ as shown in figure. Taking the origin of coordinates, O, at the centre of the first lens, the x and y coordinates of the focal point of this lens system, for a parallel beam of rays coming from the left, are given by

A
x=f1f2f1+f2, y=Δ
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B
x=f1(f2+d)f1+f2d, y=Δ2f1+f2
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C
x=f1f2+d(f1d)f1+f2d, y=Δ(f1d)f1+f2d
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D
x=f1f2+d(f1d)f1+f2d,y=0
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Solution

The correct option is C x=f1f2+d(f1−d)f1+f2−d, y=Δ(f1−d)f1+f2−d For lens −2u=−(d−f1)h0=−Δf=f21f=1v−1u1f2=1v−1−(d−f1)1v=1f2−1d−f1v=f2(d−f1)d−f1−f2= distance from lens 2.Distance form O (Lens-1) isd+f2d−f2f1d−f1−f2=d2−df1−df′2+f2A−f2f1d−f1−f2x=f1f2+d(f1−d)f1+f2−dmagnification =h1h0=vu=h1Δ=f2(d−f1)d−f1−f2−(d−f1)y1=Δ(f1−d)f1+f2−dSo option c is correct.

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