Question

Double-convex lenses are to be manufactured from a glass ofrefractive index 1.55, with both faces of the same radius ofcurvature. What is the radius of curvature required if the focal lengthis to be 20cm?

Answer 1

Given: The refractive index of the double convex lens is 1.55 , and the focal length is 20 cm.

The focal length of the lens is given as,

1 f =( μ−1 )[ 1 R 1 − 1 R 2 ]

where, the focal length of the lens is f, refractive index of the material is μ , and the radii of the curvature of the two faces of the lens are R 1 and R 2 .

By substituting the given values in the above equation, we get,

1 20 =( 1.55−1 )[ 1 R − 1 ( −R ) ] 1 20 =( 1.55−1 )[ 1 R + 1 R ] 1 20 =( 0.55 )[ 2 R ] R=22 cm

Thus, the radius of the curvature of double convex lens is 22 cm.