An object is placed in front of a convex lens such that it forms a virtual image with a magnification of 3 . When the object is moved away from the lens by a distance of 20 cm , a real image of the same magnification magnitude is formed. The focal length of the lens is ________ cm .

Step-by-step solution

For the initial virtual image, the magnification is m₁ = +3 . m₁ = v₁ u₁ = 3 v₁ = 3u₁ Using the lens formula: 1 f = 1 v₁ - 1 u₁ 1 f = 1 3u₁ - 1 u₁ = -2 3u₁ u₁ = - 2f 3 For the final real image, the magnification is m₂ = -3 . m₂ = v₂ u₂ = -3 v₂ = -3u₂ Using the lens formula again: 1 f = 1 -3u₂ - 1 u₂ = -4 3u₂ u₂ = - 4f 3 The object is moved away from the lens by 20 cm , which means the magnitude of the object distance increases by 20 cm . |u₂| - |u₁| = 20 4f 3 - 2f 3 = 20 2f 3 = 20 f = 30 cm Answer: 30