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Question
Double-convex lenses are to be manufactured from a glass of refractive index 1.55, with both faces of the same radius of curvature. What is the radius of curvature required if the focal length is to be 20 cm?
Solution
Refractive index of glass, μ = 1.55
Focal length of the double-convex lens, f = 20 cm
Radius of curvature of one face of the lens = R1
Radius of curvature of the other face of the lens = R2
Radius of curvature of the double-convex lens = R
∴ R1 = R and R2 = −R
The value of R can be calculated as:
`1/"f" = (μ - 1)[1/"R"_1 - 1/"R"_2]`
`1/20 = (1.55 - 1)[1/"R" + 1/"R"]`
`1/20 = 0.55 xx 2/"R"`
R = 0.55 × 2 × 20
∴ R = 22 cm
Hence, the radius of curvature of the double-convex lens is 22 cm.
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