27. a contact lens is made of plastic with an index of refraction of 50. The lens has an outer radius of curvature of 00 cm and an inner radius of curvature of 50 cm. What is the focal length of the lens? 28

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Lens Maker Equation:

27. A contact lens is made of plastic with an index of refraction of 1.50. The lens has an outer radius of curvature of +2.00 cm and an inner radius of curvature of +2.50 cm. What is the focal length of the lens?
28. The left face of a biconvex lens has a radius of curvature of 12.0 cm, and the right face has a radius of curvature of 18.0 cm. The index of refraction of the glass is 1.44. (a) Calculate the focal length of the lens. (b) Calculate the focal length if the radii of curvature of the two faces are interchanged.
*66. (I) A double concave lens has surface radii of 34.2 cm and 23.8 cm. What is the focal length if

*67. (I) Both surfaces of a double convex lens have radii of 31.0 cm. If the focal length is 28.9 cm, what is the index of refraction of the lens material?

*68. (II) A planoconcave lens has a focal length of What is the radius of the concave surface?

*69. (II) A Lucite planoconcave lens (see Fig. (b) below) has one flat surface and the other has What is the focal length?

*70. (II) A symmetric double convex lens with a

focal length of 25.0 cm is to be made from glass

with an index of refraction of 1.52. What should

be the radius of curvature for each surface?

*71. (II) A prescription for a corrective lens calls

for The lensmaker grinds the lens from

a “blank” with and a preformed convex

front surface of radius of curvature of 40.0 cm.

What should be the radius of curvature of the

other surface?

Solutions:

23.27 With

, the lens maker’s equation gives the focal length as

or

23.28 The lens maker’s equation is used to compute the focal
length in each case.

(a)

(b)

66. We find the focal length of the lens from

which gives

67. We find the index from the lensmaker’s equation:

. Substitute numbers:

which gives

68. We find the radius from the lensmaker’s equation:

which gives

69. We find the focal length from the lensmaker’s equation, using for Lucite:

which gives

70. We find the radius from the lensmaker’s equation, with R₁ = R and R₂ = – R.

which gives

71. We find the radius from the lensmaker’s equation:

,

which gives R₂ = – 5.6 m. Since R₂ is negative, the backside of the lens is also convex.

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