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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
1011277_90a9be4ad72a43edaa50795b5bb62d1a.png

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(f1d)f1+f2d, y=Δ(f1d)f1+f2d
For lens 2

u=(df1)h0=Δf=f2

1f=1v1u

1f2=1v1(df1)

1v=1f21df1

v=f2(df1)df1f2= distance from lens 2.

Distance form O (Lens-1) is

d+f2df2f1df1f2

=d2df1df2+f2Af2f1df1f2

x=f1f2+d(f1d)f1+f2d

magnification =h1h0=vu

=h1Δ=f2(df1)df1f2(df1)y1=Δ(f1d)f1+f2d

So option c is correct.

2005773_1011277_ans_70bf1d72bc4c4515bdeab8bd2239cd35.PNG

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