Example 3-8-13 - Maple Help
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Chapter 3: Applications of Differentiation

Section 3.8: Optimization

Example 3.8.13

Snell's law,

 sinθ1sinθ2=v1v2 

 

relates the speed of light in two adjacent media with the angles of incidence (θ1) and refraction (θ2). See Figure 3.8.13(a).

 

Derive Snell's law from Fermat's principle, namely, that light traverses the path for which travel time is least.

p1:=plottools:-arrow([0,3],[2,0],.05,.2,.1,color=red):
p2 := plottools:-arrow([2,0],[3,-4],.05,.3,.1,color=green):
p3:=plot([[2,3],[2,-4]],color=black):
p4:=plots:-textplot({[1,.25,`x`],[2.5,-4.4,`L - x`]},font=[TIMES,ROMAN,10]):
p5:=plot([[2,-4],[3,-4]],color=black,linestyle=2):
p6:=plottools:-arrow([1.2,-5],[0,-5],.1,.3,.2,color=black):
p7:=plottools:-arrow([1.8,-5],[3,-5],.1,.3,.2,color=black):
p8:=plots:-textplot([1.5,-5,"L"],font=[TIMES,ITALIC,10]):
p9:=plots:-textplot({[1.6,1.2,typeset(theta[1])],[2.2,-1.8,typeset(theta[2])]}):
p10:=plots:-textplot({[.17,1.25,typeset(a)],[1.7,-2.5,typeset(b)]}):
p11:=plots:-textplot({[.48,2.9,typeset(A)],[2.2,.2,typeset(C)],[3.3,-4,typeset(B)]}):
plots:-display([p||(1..11)], scaling=constrained, tickmarks=[[4],[-6,0,4]],view=[0..3.5,default]);

 

Figure 3.8.13(a)   Light passing from point A to point B 

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