A transparent thin film of uniform thickness and refractive index n₁ = 1.4 is coated on the convex spherical surface of radius R at one end of a long solid glass cylinder of refractive index n₂ = 1.5, as shown in the figure. Rays of light parallel to the axis of the cylinder traversing through the film from air to glass get focused at distance f₁ from the film, while rays of light traversing from glass to air get focused at distance f₂ from the film. Then

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G1 Physics · Accepted Answer

Derived solution: Step 1: For paraxial refraction at a spherical surface use n₂/v - n₁/u = (n₂ - n₁)/R, applying the Cartesian sign convention at each surface. Step 2: Test each statement independently using these relations and the data/figure. Step 3: The statements that satisfy the required optical conditions are A: |f₁| = 3R; C: |f₂| = 2R. Hence the correct answer is A,C.