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 20cm?
Answer:
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
Therefore,
R1 = R and R2 = -R
1/f = = (μ-1)(1/ R1 - 1/ R2)
1/20 = (1.55 -1) (1/R + 1/R)
1/20 = 0.55 x 2/R
R = 0.55 x 2 x 20 = 22 cm
Hence, the radius of curvature of the double-convex lens is 22 cm.
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