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Cartesian Oval

  • Thread starter fluidistic
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  • #1
fluidistic
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Homework Statement


See the picture for the situation of the problem.
I'm told that any ray starting from S and getting through the "Cartesian Oval" reach point P.
I must show that the equation of the interface curve is [tex]l_0n_1+l_i n_2=K[/tex] where K is a constant.
So far I've showed that [tex]l_0=\sqrt {x^2+y^2}[/tex] and [tex]l_i=\sqrt {y^2+(s_0 + s_i -x)^2}[/tex]. But I remain stuck as how to proceed further.
Any idea is greatly appreciated.

Homework Equations


Snell's law? I've tried something with it but didn't reach anything.
Maybe Fermat's principle?

The Attempt at a Solution


See above.
 

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Answers and Replies

  • #2
rl.bhat
Homework Helper
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Since the points S and P are fixed, the total time taken by the light to travel from S to P must be constant.
So t1 = l1/v1 and t2 = l2/v2
Now v1 = C/n1 and v2 = C/n2, where C is the velocity of the light in vacuum.
Hence find t = t1 + t2 = ...........?
 
Last edited:
  • #3
fluidistic
Gold Member
3,654
100


Since the points S and P are fixed, the total time taken by the light to travel from S to P must be constant.
So t1 = l1/v1 and t2 = l2/v2
Now v1 = C/n1 and v2 = C/n2, where C is the velocity of the light.
Hence find t = t1 + t2 = ...........?
Thank you so much! Really bright and not complicated. Yet I totally missed it.
Problem solved!
 

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