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Two thin convex lenses of length f1 andf2 are separated by a horizontal distance d (where d<f1 and d<f2 ), and their centers are displaced by a vertical separation Δ as shown in the figure. Taking the origin of coordinates, O at the center of left 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

156341_f5b978b95f8f4de69b6d3c77a598c91c.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
The light coming from infinity is refracted from first lens to form image at the focus of the lens, that is, at a distance of f1 from the first lens.
This image acts as object for second lens at a distance of f1d from it.
Hence from the lens equation,

1v=1f2+1u

v=f2(f1d)f1+f2d

Hence the x-coordinate of this final image formed =d+v

x=f1f2+d(f1d)f1+f2d

The magnification caused by the second lens is:

vu=f2f1+f2d=h2h1=ΔΔ

y=ΔΔ=Δ(f1d)f1+f2d

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