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$wrapped $paragraphs $paragraph $words $word $len $wlen String variable containing the wrapped text to be returned Array containing the separate paragraphs as determined by \n characters String containing an individual paragraph being processed Array of all words in a paragraph String containing the current word being processed Numeric variable containing the length of the current line Numeric variable containing the length of the next word to be processed

located twice as far from the mirror as the object Prove your answer mathematically Calculate the focal length as a function of object position for this placement

2 Draw and label a ray diagram showing the location of the object if the image is located twice as far

from the mirror as the focal point Prove your answer mathematically Calculate the image height as a function of the object height for this placement

Figure 17-14 A convex mirror always produces virtual images that are upright and smaller compared to the object

The plug-in works by first splitting the text passed to it into separate paragraphs using the PHP explode() function with an argument of \n, which is the newline character What this function does is return an array of substrings based on splitting the original string each time a \n is encountered The function returns these paragraphs in the array $paragraphs A foreach loop is then entered passing $paragraphs as the input, and then each iteration of the loop places one paragraph at a time into the string variable $paragraph

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In the first part of this chapter, you learned that the inner surface of a shiny spoon acts as a concave mirror If you turn the spoon around, the outer surface acts as a convex mirror, a reflective surface with edges that curve away from the observer What do you see when you look at the back of a spoon You see an upright, but smaller image of yourself Properties of a spherical convex mirror are shown in Figure 17-14 Rays reflected from a convex mirror always diverge Thus, convex mirrors form virtual images Points F and C are behind the mirror In the mirror equation, f and di are negative numbers because they are both behind the mirror The ray diagram in Figure 17-14 represents how an image is formed by a spherical convex mirror The figure uses two rays, but remember that there are an infinite number of rays Ray 1 approaches the mirror parallel to the principal axis The reflected ray is drawn along a sight line from F through the point where ray 1 strikes the mirror Ray 2 approaches the mirror on a path that, if extended behind the mirror, would pass through F The reflected part of ray 2 and its sight line are parallel to the principal axis The two reflected rays diverge, and the sight lines intersect behind the mirror at the location of the image An image produced by a single convex mirror is a virtual image that is upright and smaller compared to the object The magnification equation is useful for determining the apparent dimensions of an object as seen in a spherical convex mirror If you know the diameter of an object, you can multiply by the magnification fraction to see how the diameter changes You will find that the diameter is smaller, as are all other dimensions This is why the objects appear to be farther away than they actually are for convex mirrors Field of view It may seem that convex mirrors would have little use because the images that they form are smaller than the objects However, this property of convex mirrors does have practical uses By forming smaller images, convex mirrors enlarge the area, or field of view, that an observer sees, as shown in Figure 17-15 Also, the center of this field of view is visible from any angle of an observer off the principal axis of the mirror; thus, the field of view is visible from a wide perspective For this reason, convex mirrors often are used in cars as passenger-side rearview mirrors.

Figure 17-15 Convex mirrors produce images that are smaller than the objects This increases the field of view for observers