A symmetric biconvex lens is made of glass of refractive index 1.4. The two spherical surfaces have equal radius of curvature R in magnitude. What is the ratio f / R, where f is the focal length of the lens in air?
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Question

A symmetric biconvex lens is made of glass of refractive index 1.4. The two spherical surfaces have equal radius of curvature R in magnitude. What is the ratio f / R, where f is the focal length of the lens in air?

Options

G1 Physics · Accepted Answer

For a thin lens in air, 1 ÷ f = (μ-1)[1 ÷ R₁-1 ÷ R₂]. For a symmetric biconvex lens, R₁ = +R, R₂ = -R. Therefore, 1 ÷ f = (1.4-1)[1 ÷ R-1 ÷ (-R)] = 0.4(2 ÷ R) = 0.8 ÷ R. Hence, f ÷ R = 1 ÷ 0.8 = 1.25. Correct option: D.