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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.
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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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