A symmetric bi-convex lens has equal radii of curvature of magnitude 1/6 cm on its two surfaces. It is to be replaced by another convex lens of the same material and the same power, but with unequal radii R₁ and R₂. Which pair of radius magnitudes can produce the same power?
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Question

A symmetric bi-convex lens has equal radii of curvature of magnitude 1/6 cm on its two surfaces. It is to be replaced by another convex lens of the same material and the same power, but with unequal radii R₁ and R₂. Which pair of radius magnitudes can produce the same power?

Options

G1 Physics · Accepted Answer

For a thin lens in air, 1/f = (μ-1)(1/R₁ - 1/R₂). For a bi-convex lens, one radius is positive and the other negative, so in terms of their positive magnitudes the curvature contribution is the sum of reciprocals. Original symmetric lens: 1/R + 1/R = 6 + 6 = 12 cm⁻¹. The replacement must satisfy 1/R₁ + 1/R₂ = 12 cm⁻¹. Check option C: R₁ = 1/5 cm, R₂ = 1/7 cm. Then 1/R₁ + 1/R₂ = 5 + 7 = 12 cm⁻¹. Therefore it has the same power. Correct option: C.