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For n1 = 2.15 and n2 = 1.26, what is the critical angle so that all of

  1. Oct 30, 2011 #1
    For n1 = 2.15 and n2 = 1.26, what is the critical angle so that all of the incident light, from medium 1 to medium 2 is reflected?



    Im using Sin ic = n1/n2



    For Sin ic i get =1.706

    But the reverse Sin of that comes up math error?

    HELP
     
  2. jcsd
  3. Oct 30, 2011 #2

    Doc Al

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    Staff: Mentor

    Re: Confused?

    You're mixing up n1 and n2. Start from Snell's law and derive the expression for total internal reflection.
     
  4. Oct 30, 2011 #3
    Re: Confused?

    Thank you!

    I need help rearranging the equation too, im finding it impossible!

    Nmax = 4a/lamda x sqaureroot (N1^2 - N2^2)

    I need to find n2
     
  5. Oct 30, 2011 #4
    Re: Confused?

    Firstly you gave this equation:

    Nmax = 4a/lamda x sqaureroot (N1^2 - N2^2)

    Am I correct to think this is equivalent?

    [itex] N_{max}=\frac{4a}{λ} \sqrt{n_{1}^{2}-n_{2}^{2}} [/itex]

    (I would suggest in future as opposed to using "x" to indicate multiplies, I would use "*". Simply for clarity)

    If this is the case begin by squaring both sides of the equation, and then attempt to isolate the [itex] n_{2} [/itex] term.
     
  6. Oct 30, 2011 #5
    Re: Confused?

    I have no idea how to rearrange this.

    i know by squaring both sides the sqaure root will disappear. But on the other side Nmax = 1.

    How does it rearrange so i get a positive number to square root to find n2?
     
  7. Oct 30, 2011 #6

    Doc Al

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    Staff: Mentor

    Re: Confused?

    So?
    Start by squaring both sides and then go from there.
     
  8. Oct 30, 2011 #7
    Re: Confused?

    Find an equation for n2, and then try to understand what this means.
     
  9. Oct 30, 2011 #8
    Re: Confused?

    Im so confused :(

    every time i try to rearrange to find n2 i get math error!
     
  10. Oct 30, 2011 #9

    Doc Al

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    Staff: Mentor

    Re: Confused?

    Show what you did symbolically, step by step.
     
  11. Oct 30, 2011 #10
    Re: Confused?

    This is due to you doing it on a calculator. Rearrange it on paper, so that you have

    n2= ...
     
  12. Oct 30, 2011 #11
    Do I have to multiply out the brackets?
     
  13. Oct 30, 2011 #12
    Re: Confused?

    The term [itex] \sqrt{n_{1}^{2}-n_{2}^{2}}=\sqrt{(n_{1}^{2}-n_{2}^{2})} [/itex]

    So by squaring you will get

    [itex] N_{max}^{2}=(\frac{4a}{λ})^{2} (n_{1}^{2}-n_{2}^{2}) [/itex]

    It would be more convenient if you multiplied both sides of [itex] (\frac{λ}{4a})^{2} [/itex] rather than multiplying out the brackets.
     
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