document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=130030>Question 130030</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I have this last story problem to do and am confused, can someone help?\r<BR>\n" );
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document.write( "Use the formula 1 over f = 1 over o + 1 over i to find the image distance i for an object that is 2,000,000 mm from a 250-mm telephoto lens.\r<BR>\n" );
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document.write( "So confused, can someone help? Thanks </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #94980 by </B><A HREF=/tutors/aboutme.mpl?userid=bucky><B>bucky(2189)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bucky><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=94980\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Given the formula for a lens:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2Ff+=+1%2Fo+%2B+1%2Fi ALIGN=MIDDLE  ALT=\"1%2Ff+=+1%2Fo+%2B+1%2Fi\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "In which f is the focal length of the lens, o is the object distance from the lens, and <BR>\n" );
document.write( "i is the image distance from the lens.  <BR>\n" );
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document.write( "For this problem, you are told that f, the focal length of the lens, if 250 mm and that o<BR>\n" );
document.write( "the object distance from the lens is 2,000,000 mm. (The object is 2,000 meters away, which<BR>\n" );
document.write( "is a long distance compared to the focal length of the lens.)<BR>\n" );
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document.write( "All units in this equation will be mm. Substitute the two values you are given (one for f<BR>\n" );
document.write( "and one for o) and you have:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F250+=+1%2F2000000+%2B+1%2Fi ALIGN=MIDDLE  ALT=\"1%2F250+=+1%2F2000000+%2B+1%2Fi\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Let's get rid of the denominator 2000000 by multiplying both sides (all terms) of this equation<BR>\n" );
document.write( "by 2000000 and the equation then becomes:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2000000%2F250+=+1+%2B+2000000%2Fi ALIGN=MIDDLE  ALT=\"2000000%2F250+=+1+%2B+2000000%2Fi\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Do the division on the left side by dividing 250 into 2000000 and the equation becomes:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8000+=+1+%2B+2000000%2Fi ALIGN=MIDDLE  ALT=\"8000+=+1+%2B+2000000%2Fi\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Get rid of the 1 on the right side by subtracting 1 from both sides and this reduces the<BR>\n" );
document.write( "equation to:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7999+=+2000000%2Fi ALIGN=MIDDLE  ALT=\"7999+=+2000000%2Fi\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Get rid of the denominator i on the right side by multiplying both sides of the equation (all terms)<BR>\n" );
document.write( "by i to get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7999i+=+2000000 ALIGN=MIDDLE  ALT=\"7999i+=+2000000\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Solve for i by dividing both sides of the equation by 7999 and you have:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=i+=+2000000%2F7999 ALIGN=MIDDLE  ALT=\"i+=+2000000%2F7999\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Do the division on the right side (use a calculator) and you find that the image distance is<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=i+=+250.0312539 ALIGN=MIDDLE  ALT=\"i+=+250.0312539\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "So the answer is that the image distance from the lens is about 250.03 mm.<BR>\n" );
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document.write( "If you are into physics and science, what does this tell you?  It says that as long as the<BR>\n" );
document.write( "object is far away from the lens, the image will always be about 250 mm from the lens. Therefore,<BR>\n" );
document.write( "the image will be pretty much in focus if the film or the digital sensors plates for digital<BR>\n" );
document.write( "cameras are located about 250 mm behind the lens. This would be a pretty good sized camera<BR>\n" );
document.write( "since 250 meters behind the lens is nearly 10 inches, so the camera would be around<BR>\n" );
document.write( "10 inches deep.\r<BR>\n" );
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document.write( "Maybe this will make sense to you. It does to serious photographers.<BR>\n" );
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document.write( "Hope this helps you to learn a little about math and also some about the physical <BR>\n" );
document.write( "characteristics of lenses.<BR>\n" );
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