An equiconvex lens is cut into halves along (i) XX′ and (ii) YY′ as shown in the figure. Let f, f′, f″ denote focal lengths of the complete lens, each half in case (i), and each half in case (ii), respectively. Which relation is correct?
Options

Question

An equiconvex lens is cut into halves along (i) XX′ and (ii) YY′ as shown in the figure. Let f, f′, f″ denote focal lengths of the complete lens, each half in case (i), and each half in case (ii), respectively. Which relation is correct?

Options

G1 Physics · Accepted Answer

Step 1: Cutting through the principal axis reduces the aperture only; the radii of refracting surfaces remain the same, so f′ = f. Step 2: Cutting perpendicular to the axis creates two plano-convex lenses, each with half the original power of an equiconvex lens, so f″ = 2f. Final answer: (A) f′ = f and f″ = 2f.