Double-convex lenses are to be manufactured from a glass of refractive index 1.55, with both faces of the same radius of curvature. - Physics

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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?

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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" = (μ - 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 × 2 × 20 = 22 cm

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

Concept: Refraction
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Chapter 9: Ray Optics and Optical Instruments - Exercise [Page 344]

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NCERT Physics Class 12
Chapter 9 Ray Optics and Optical Instruments
Exercise | Q 9.7 | Page 344
NCERT Physics Class 12
Chapter 9 Ray Optics and Optical Instruments
Exercise | Q 7 | Page 346

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