. In the displacement method for determining the focal length of a convex lens, the lens is displaced by distance x to again obtain a sharp image on the screen. If the magnification in two positions a

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. In the displacement method for determining the focal length of a convex lens, the lens is displaced by distance x to again obtain a sharp image on the screen. If the magnification in two positions are m 1 ​ and m 2 ​ respectively, the focal length of the lens is

TestHub · Accepted Answer

x = L − 2 y y = 2 L − x ​ L − y = L − 2 ( L − x ) ​ = 2 L + x ​ v 1 ​ + u 1 ​ = f 1 ​ L − x 2 ​ + L + x 2 ​ = f 1 ​ ⇒ f = 4 L L 2 − x 2 ​ m 1 ​ = L − x L + x ​ ; m 2 ​ = − L + x ( L − x ) ​ m 1 ​ − m 2 ​ = − [ L 2 − x 2 4 Lx ​ ] ∣ m 1 ​ − m 2 ​ ∣ x ​ = 4 Lx x ​ × ( L 2 − x 2 ) = f ​

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