A double convex lens is made of glass of refractive index `1.55` with both faces of same radius of curvature. Find the radius of curvature required, if focal length is `20 cm`.

Options

A. 22 cm
B. 44 cm
C. 11 cm
D. 33 cm

Answer

A

Explanation

Refractive index of glass, `mu=1.55`
Focal length of the double-convex lens, f=20cm
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 R_(1) = R and R_(2)= -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 xx 2/R`
`therefore R=0.5 xx 2 xx 20 = 22 cm`
Hence, the radius of curvature of the double-convex lens is 22 cm.