Three identical convex lenses each of focal length $f$ are placed in a straight line separated by a distance $f$ from each other. An object is located at $f /2$ in front of the leftmost lens. Then,

Question

Three identical convex lenses each of focal length f are placed in a straight line separated by a distance f from each other. An object is located at f /2 in front of the leftmost lens. Then,

TestHub · Accepted Answer

Hint : For first lens ​ u = − 2 f ​ f 1 ​ = v 1 ​ − u 1 ​ ⇒ f 1 ​ = v 1 ​ − 2 − f ​ 1 ​ ⇒ v 1 ​ = f 1 ​ − f 2 ​ ⇒ v 1 ​ = f − 1 ​ v = − f m 1 ​ = u v ​ = 2 − f ​ − f ​ = 2 ​ For second lens u = − ( f + f ) = − 2 f ​ v 1 ​ − u 1 ​ = f 1 ​ ⇒ v 1 ​ − − 2 f 1 ​ = f 1 ​ ⇒ v 1 ​ = f 1 ​ − 2 f 1 ​ ⇒ v 1 ​ = 2 f 1 ​ v = 2 f m 1 ​ = u v ​ = − 2 f 2 f ​ = − 1 ​ For third lens ​ u = f f = f v 1 ​ − u 1 ​ = f 1 ​ ⇒ v 1 ​ = f 1 ​ + u 1 ​ ⇒ v 1 ​ = f 1 ​ + f 1 ​ ⇒ v 1 ​ = f 2 ​ ⇒ v = 2 f ​ ​ m 3 ​ = u v ​ = f 2 f ​ ​ = 2 1 ​ Total magnification = m 1 ​ m 2 ​ m 3 ​ = 2 × ( − 1 ) × 2 1 ​ = − 1

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