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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? - Physics

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,  mu = 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

`:.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`

`:. R = 0.55 xx 2/R`

Hence, the radius of curvature of the double-convex lens is 22 cm

Concept: Refraction
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NCERT Class 12 Physics Textbook
Chapter 9 Ray Optics and Optical Instruments
Q 7 | Page 346
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