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? *69. (II) A Lucite planoconcave lens (see Fig. (b) below) has one flat surface and the other has What is the focal length? with an index of refraction of 1.52. What should be the radius of curvature for each surface? a “blank” with and a preformed convex front surface of radius of curvature of 40.0 cm. 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. |