document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=279631>Question 279631</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 1.   The lens equation for a camera is  1/f = 1/di + 1/do , where f is the focal length of the lens, di is the distance between the lens and the film, and do is the distance between the lens and the object. For a certain camera, an object that is 18 cm from the lens is in focus when the lens is 9 cm from the film. What is the focal length of the lens?<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #203246 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=203246\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 1/f = 1/di + 1/do<BR>\n" );
document.write( "f is the focal length of the lens<BR>\n" );
document.write( "di is the distance between the lens and the film.<BR>\n" );
document.write( "do is the distance between the lens and the object.\r<BR>\n" );
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document.write( "object is 18 cm from the lens.<BR>\n" );
document.write( "lens is 9 cm from the film.\r<BR>\n" );
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document.write( "do = 18<BR>\n" );
document.write( "di = 9\r<BR>\n" );
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document.write( "1/f = 1/9 + 1/18\r<BR>\n" );
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document.write( "1/9 is the same as 2/18 so this equation becomes:\r<BR>\n" );
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document.write( "1/f = 2/18 + 1/18 = 3/18\r<BR>\n" );
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document.write( "you have:\r<BR>\n" );
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document.write( "1/f = 3/18\r<BR>\n" );
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document.write( "since this is in the form of a ratio, you can cross multiply to get:\r<BR>\n" );
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document.write( "3f = 18\r<BR>\n" );
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document.write( "divide both sides of this equation by 3 to get:\r<BR>\n" );
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document.write( "f = 6\r<BR>\n" );
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document.write( "your answer is that the focal length of the lens is 6.\r<BR>\n" );
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document.write( "you confirm by plugging that value into the equation to see that it is true.\r<BR>\n" );
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document.write( "the equation is 1/f = 1/di + 1/do\r<BR>\n" );
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document.write( "we had di = distance from lens to the film = 9 cm.\r<BR>\n" );
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document.write( "we had do = distance from object to the lens = 18 cm.\r<BR>\n" );
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document.write( "we have f = 6\r<BR>\n" );
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document.write( "equation becomes:\r<BR>\n" );
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document.write( "1/6 = 1/9 + 1/18\r<BR>\n" );
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document.write( "convert all to denominator of 18 to get:\r<BR>\n" );
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document.write( "3/18 = 2/18 + 1/18 which becomes:\r<BR>\n" );
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document.write( "3/18 = 3/18 which is true confirming that the value of f = 6 is good.\r<BR>\n" );
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