Class 12 Physics
CBSE and UP Board
Ray Optics and Optical Instruments
Chapter-9 Exercise 9.7
NCERT Solutions for Class 12 Physics Chapter 9 Question-7
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 20 cm?
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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
The value of R can be calculated as:
1/f = (μ-1) [1/R1 -1/R2]
1/20 = (1.55 -1)[1/R + 1/R]
1/20 = 0.55 x 2/R
Therefore,
R = 0.55 x 2 x 20 = 22cm
Hence, the radius of curvature of the double-convex lens is 22 cm.