An object placed 40 cm in front of a thin convex lens is moved to 60 cm from the lens. If the focal length of the lens is 30 cm the ratio of magnification of the image at the initial position to the final position is:

Step-by-step solution

Using the lens formula, the magnification produced by a lens is given by m = f f + u . For the initial position, the object distance is u₁ = -40 cm and the focal length is f = 30 cm. m₁ = 30 30 + (-40) = 30 -10 = -3 For the final position, the object distance is u₂ = -60 cm. m₂ = 30 30 + (-60) = 30 -30 = -1 The ratio of the magnification at the initial position to the final position is: m₁ m₂ = -3 -1 = 3 1 Thus, the required ratio is 3:1 . Answer: 3:1