Match List-I with List-II for the equivalent focal length of two thin lenses placed in contact. The focal lengths of the lenses are given in terms of a positive magnitude f . List-I (Lens combination) List-II (Equivalent focal length) A. Convex f and Convex f I. f B. Convex f and Concave f II. -f C. Convex f and Concave f/2 III. Infinite D. Convex f/2 and Concave f IV. f/2 Choose the correct answer from the options g

Step-by-step solution

For two thin lenses in contact, the equivalent focal length F is given by 1 F = 1 f₁ + 1 f₂ . By sign convention, the focal length of a convex lens is positive, and that of a concave lens is negative. A. Convex f and Convex f : 1 F = 1 f + 1 f = 2 f F = f 2 (Matches IV) B. Convex f and Concave f : 1 F = 1 f - 1 f = 0 F = (Matches III) C. Convex f and Concave f/2 : 1 F = 1 f - 2 f = - 1 f F = -f (Matches II) D. Convex f/2 and Concave f : 1 F = 2 f - 1 f = 1 f F = f (Matches I) Therefore, the correct matching is A-IV