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A lens is a piece of transparent material, such as glass or plastic, that is used to focus light and form an image Each of a lens s two faces might be either curved or flat The lens in Figure 18-9a is called a convex lens because it is thicker at the center than at the edges A convex lens often is called a converging lens because when surrounded by material with a lower index of refraction it refracts parallel light rays so that the rays meet at a point The lens in Figure 18-9b is called a concave lens because it is thinner in the middle than at the edges A concave lens often is called a diverging lens because when surrounded by material with a lower index of refraction rays passing through it spread out When light passes through a lens, refraction occurs at the two lens surfaces Using Snell s law and geometry, you can predict the paths of rays passing through lenses To simplify such problems, assume that all refraction occurs on a plane, called the principal plane, that passes through the center of the lens This approximation, called the thin lens model, applies to all the lenses that you will learn about in this chapter section Lens equations The problems that you will solve involve spherical thin lenses, lenses that have faces with the same curvature as a sphere Based on the thin lens model, as well as the other simplifications used in solving problems for spherical mirrors, equations have been developed that look exactly like the equations for spherical mirrors The thin lens equation relates the focal length of a spherical thin lens to the object position and the image position Thin Lens Equation



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The inverse of the focal length of a spherical lens is equal to the sum of the inverses of the image position and the object position

The magnification equation for spherical mirrors used in 17 also can be used for spherical thin lenses It is used to determine the height and orientation of the image formed by a spherical thin lens Magnification m





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Answer (for Objective 34): C, D, and F are correct The "\\d" tells the split() method to split Strings whenever a digit is encountered The "\\s" tells the split() method to split Strings whenever a whitespace character is encountered Because a standalone "" (dot) is a predefined metacharacter (like \d or \s), the "\\" tells the split method to split Strings whenever the character "" is encountered A is incorrect because "s" characters are viewed as splitting characters and are removed from the output B is incorrect because "d" characters are viewed as splitting characters E is incorrect because the "\\w" tells the split() method to use letters, digits, and the underscore character as splitting characters

The magnification of an object by a spherical lens, defined as the image height divided by the object height, is equal to the negative of the image position divided by the object position

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Figure 18-9 A convex lens causes rays of light to converge (a) A concave lens causes rays of light to diverge (b)

Table 18-2

49 Given the design implied by this partially implemented class:

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Properties of a Single Spherical Lens System Lens Type f do Convex 2f f do do do 0 do 2f f 0 2f di di f di di 2f do 0 f m Reduced Inverted Enlarged Inverted Enlarged Image Real Real Virtual

(negative)

(negative)

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