document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1163329>Question 1163329</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If you are in shallow water and look at an object below the surface of the water, <BR>\n" );
document.write( "the object will look farther away from you than it really is. This is because as light passes <BR>\n" );
document.write( "through air and water it bends or refracts the light rays. The index of refraction for water is 1.33.<BR>\n" );
document.write( "This is the ratio of the sine of theta 1 and the sine of theta 2.\r<BR>\n" );
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document.write( "a)You are in 2 feet of water in the shallow end of a pool. You look down at some goggles at angle <BR>\n" );
document.write( "(theta=60) degrees measured from a line perpendicular to the surface of the water. Find (theta 2 ) \r<BR>\n" );
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document.write( "b) Find the distances x and y <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 #854592 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5396)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=854592\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I agree with ikleyn and CPhill, but I would like to draw and overexplain as usual.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28350%2C300%2C-3%2C4%2C-1%2C5%2C%0D%0Ablue%28line%28-3%2C2%2C4%2C2%29%29%2Cline%28-3%2C0%2C4%2C0%29%2C%0D%0Aline%28-2.6%2C3.5%2C0%2C2%29%2C+green%28line%280%2C2%2C3.464%2C0%29%29%2C%0D%0Aline%280%2C2%2C1.716%2C0%29%2Crectangle%280%2C0%2C0.2%2C0.2%29%2C%0D%0Ared%28line%280%2C0%2C0%2C5%29%29%2Carc%280%2C2%2C3%2C3%2C-150%2C-90%29%2C%0D%0Aarc%280%2C2%2C3%2C3%2C49.37%2C90%29%2Clocate%28-0.7%2C3.2%2Ctheta%29%2C%0D%0Alocate%280.25%2C1%2Ctheta%29%2Clocate%28-0.54%2C3.1%2C1%29%2C%0D%0Alocate%280.45%2C0.9%2C2%29%2Ccircle%28-2.6%2C3.5%2C0.1%29%2Ccircle%281.716%2C0%2C0.1%29%2C%0D%0Agreen%28circle%283.464%2C0%2C0.1%29%29%2Carc%280%2C2%2C3.4%2C3.4%2C30%2C90%29%2C%0D%0Alocate%281.4%2C1%2Ctheta%29%2Clocate%281.6%2C0.9%2C1%29%2C%0D%0Alocate%28-2.8%2C4.9%2Ceye%29%2Carrow%28-2.6%2C4.6%2C-2.6%2C3.6%29%2C%0D%0Alocate%28-0.9%2C1.2%2C2ft%29%2Carrow%28-1%2C1.3%2C-1%2C0%29%2Carrow%28-1%2C0.7%2C-1%2C2%29%2C%0D%0Aarrow%281.9%2C-0.2%2C0%2C-0.2%29%2Carrow%281.5%2C-0.2%2C3.464%2C-0.2%29%2C%0D%0Aarrow%281.3%2C-0.6%2C0%2C-0.6%29%2Carrow%280.5%2C-0.6%2C1.716%2C-0.6%29%2C%0D%0Alocate%280.3%2C-0.6%2C1.716ft%29%2Clocate%282%2C-0.2%2C3.464ft%29%2C%0D%0Aarrow%281.716%2C-0.8%2C1.716%2C-0.1%29%2Clocate%281.5%2C-0.7%2Cgoggles%29%2C%0D%0Agreen%28arrow%283.464%2C2.9%2C3.464%2C0.1%29%29%2Clocate%283.1%2C3.1%2Cgreen%28ghost%29%29%2C%0D%0Alocate%282.8%2C3.4%2Cgreen%28goggles%29%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%2820%2C30%2C0%2C0.4%2C-0.6%2C0%2C%0D%0Alocate%280.39%2C0%2Ctheta%29%0D%0A%29 ALIGN=MIDDLE  ALT=\"drawing%2820%2C30%2C0%2C0.4%2C-0.6%2C0%2C%0D%0Alocate%280.39%2C0%2Ctheta%29%0D%0A%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1 ALIGN=MIDDLE  ALT=\"1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%22=%22 ALIGN=MIDDLE  ALT=\"%22=%22\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=60%5Eo ALIGN=MIDDLE  ALT=\"60%5Eo\"   DISABLED_style= \"max-width:90%; height:auto;\" > (given)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%2820%2C30%2C0%2C0.4%2C-0.6%2C0%2C%0D%0Alocate%280.39%2C0%2Ctheta%29%0D%0A%29 ALIGN=MIDDLE  ALT=\"drawing%2820%2C30%2C0%2C0.4%2C-0.6%2C0%2C%0D%0Alocate%280.39%2C0%2Ctheta%29%0D%0A%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" > value calculated based on Snell's Law: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%22sin%28%22 ALIGN=MIDDLE  ALT=\"%22sin%28%22\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=theta ALIGN=MIDDLE  ALT=\"theta\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%221%29%22 ALIGN=MIDDLE  ALT=\"%221%29%22\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%22=%22 ALIGN=MIDDLE  ALT=\"%22=%22\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%2A%22sin%28%22 ALIGN=MIDDLE  ALT=\"n%2A%22sin%28%22\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=theta ALIGN=MIDDLE  ALT=\"theta\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%222%29%22 ALIGN=MIDDLE  ALT=\"%222%29%22\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%2860%5Eo%29 ALIGN=MIDDLE  ALT=\"sin%2860%5Eo%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%22=%22 ALIGN=MIDDLE  ALT=\"%22=%22\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1.33%2A%22sin%28%22 ALIGN=MIDDLE  ALT=\"1.33%2A%22sin%28%22\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=theta ALIGN=MIDDLE  ALT=\"theta\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%222%29%22 ALIGN=MIDDLE  ALT=\"%222%29%22\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%283%29%2F2 ALIGN=MIDDLE  ALT=\"sqrt%283%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%22=%22 ALIGN=MIDDLE  ALT=\"%22=%22\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1.33%2A%22sin%28%22 ALIGN=MIDDLE  ALT=\"1.33%2A%22sin%28%22\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=theta ALIGN=MIDDLE  ALT=\"theta\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%222%29%22 ALIGN=MIDDLE  ALT=\"%222%29%22\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%283%29%2F2%2F1.33 ALIGN=MIDDLE  ALT=\"sqrt%283%29%2F2%2F1.33\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%22=%22 ALIGN=MIDDLE  ALT=\"%22=%22\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%22sin%28%22 ALIGN=MIDDLE  ALT=\"%22sin%28%22\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=theta ALIGN=MIDDLE  ALT=\"theta\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%222%29%22 ALIGN=MIDDLE  ALT=\"%222%29%22\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "From that we can find <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=theta ALIGN=MIDDLE  ALT=\"theta\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%222%29%22 ALIGN=MIDDLE  ALT=\"%222%29%22\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%22=%22 ALIGN=MIDDLE  ALT=\"%22=%22\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%2840.63%5Eo%29 ALIGN=MIDDLE  ALT=\"highlight%2840.63%5Eo%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > (rounded)<BR>\n" );
document.write( "We can also find <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%22cos%28%22 ALIGN=MIDDLE  ALT=\"%22cos%28%22\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=theta ALIGN=MIDDLE  ALT=\"theta\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%222%29%22 ALIGN=MIDDLE  ALT=\"%222%29%22\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%22tan%28%22 ALIGN=MIDDLE  ALT=\"%22tan%28%22\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=theta ALIGN=MIDDLE  ALT=\"theta\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%222%29%22 ALIGN=MIDDLE  ALT=\"%222%29%22\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and the distance<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2ft%2A%22tan%28%22 ALIGN=MIDDLE  ALT=\"2ft%2A%22tan%28%22\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=theta ALIGN=MIDDLE  ALT=\"theta\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%222%29%22=highlight%281.716ft%29 ALIGN=MIDDLE  ALT=\"%222%29%22=highlight%281.716ft%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > (rounded)<BR>\n" );
document.write( "Independently of refraction, we can find the distance<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2ft%2A%22tan%28%22 ALIGN=MIDDLE  ALT=\"2ft%2A%22tan%28%22\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=theta ALIGN=MIDDLE  ALT=\"theta\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%221%29%22 ALIGN=MIDDLE  ALT=\"%221%29%22\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%22=%22 ALIGN=MIDDLE  ALT=\"%22=%22\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2ft%2Atan%2860%5Eo%29=2ft%2Asqrt%283%29=highlight%283.464ft%29 ALIGN=MIDDLE  ALT=\"2ft%2Atan%2860%5Eo%29=2ft%2Asqrt%283%29=highlight%283.464ft%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > (rounded) </SPAN>\n" );
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