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Question
A double convex lens is made of a glass of refractive index 1.55, with both faces of the same radius of curvature. Find the radius of curvature required, if the focal length is 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=(mu-1)[1/R_1-1/R_2]`
`1/20=(1.55-1)[1/R+1/R]`
`1/20=(0.55)[2/R]`
`therefore R=22 cm`
Hence , the radius of curvature of the double-convex lens is 22 cm
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