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Question

Two thin convex lenses of focal length f1and f2 are separated by a horizontal distance d (where d<f1,d<f2) and their centers are displaced by a vertical separation Δ as shown in figure.

Taking the origin of coordinates O at the center 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=Δf1+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=Δ(f1d)f1+f2d
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Solution

The correct option is C x=f1f2+d(f1d)f1+f2d, y=Δ(f1d)f1+f2d
patiently use lens formula for individual lens one by one and get the final position of the image. The total distance would be d+v(final) and which will come as f1f2+d(f1d)f1+f2d.
for finding y, use magnification formula and get Δ(f1d)f1+f2d
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