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A thin plano-convex lens of focal length...

A thin plano-convex lens of focal length f is split into two halves. One of the halves is shifted along the optical axis as shown in figure. The sepration between object and image planes is `1.8m.` The magnification of the image formed by one of the half lens is `2.` Find the focal length of the lens and separation between the two halves. Draw the ray diagram for image formation.

Text Solution

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since the magnification for `L_(1)` is 2
`+> v/u = -2`
`implies ((D+d)/2)/(- (D-d)/2) = -2`
`implies (D+d)/(D-d) =2`
`implies D=1.8m, d=0.6 m.`
`f= (D^(2)-d^(2))/(4D) = ((1.8+0.6)(1.8-0.6))/(4xx0.8) = 0.4 m`
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